High Energy Solutions Research Articles

Optimized K+ Deposition Dynamics via Potassiphilic Porous Interconnected Mediators Coordinated by Single-Atom Iron for Dendrite-Free Potassium Metal Batteries.

Potassium metal batteries are emerging as a promising high-energy density storage solution, valued for their cost-effectiveness and low electrochemical potential. However, understanding the role of potassiphilic sites in nucleation and growth remains challenging. This study introduces a single-atom iron, coordinated by nitrogen atoms in a 3D hierarchical porous carbon fiber (Fe─N-PCF), which enhances ion and electron transport, improves nucleation and diffusion kinetics, and reduces energy barriers for potassium deposition. Molten potassium infusion experiments confirm the Fe─N-PCF's strong potassiphilic properties, accelerating adsorption kinetics and improving potassium deposition performance. According to the Scharifker-Hills model, traditional carbon fiber substrates without potassiphilic sites cause 3D instantaneous nucleation, leading to dendritic growth. In contrast, the integration of single-atom and hierarchical porosity promotes uniform 3D progressive nucleation, leading to dense metal deposition, as confirmed by dimensionless i2/imax 2 versus t/tmax plots and real-time in situ optical microscopy. Consequently, in situ X-ray diffraction demonstrated stable potassium cycling for over 1900 h, while the Fe─N-PCF@K||PTCDA full cell retained 69.7% of its capacity after 2000 cycles (72 mAh g-1), with a low voltage hysteresis of 0.876V, confirming its strong potential for high energy density and extended cycle life, paving the way for future advancements in energy storage technology.

First-Principles Study on Lithiation Process of Sio Anode for Li-Ion Batteries

Lithium-ion secondary batteries (LIB) with a high energy density have been developed mainly for use in small mobile devices. In recent years, the high capacity of LIB has become important for automobile applications. One possible high-energy density solution is the use of high-capacity negative electrodes fabricated from tin, silicon, or other materials, and a-SiO materials have been already commercialized. However, a-SiO materials has the issue of capacity degradation during charge-discharge cycles. In particular, it is speculated that the structural change during charging process causes the capacity degradation, but the detail has not been clarified yet. Therefore, in this study, we clarify the local structural changes in a-SiO up to full charge using first-principles calculations.In our previous study [1], a-SiO models were generated using classical molecular dynamics (MD) simulations with neural network potentials.Using one of these models, we explore the lithiation process of a-SiO using first-principles calculations with SIESTA code [2]. The simplest method to obtain a-Li x SiO model is to melt an initial structure in which Li atoms are randomly arranged at high temperature and then cool it. But it was found that this process could not reproduce the actual charge process and Li atoms should be placed at stable sites. Therefore, we developed a computational code with which stable sites of Li atoms can be searched efficiently using Bayesian optimization.Fig. 1 shows Li-inserted models at (a) 0%, (b) 55% and (c) 100% SoC (State of Charge). Li atoms are gradually inserted into the SiOx phase in the initial state of charging, and inserted into the Si phase over 20% SoC. These results are consistent with previous experimental results [3]. One Li6O octahedron can be seen in the model at 55% SoC, and the number of Li6O octahedra increases to five in the model at 100% SoC. The formation of Li6O octahedra during charging is irreversible, which is considered to cause the capacity degradation. To prevent capacity degradation, it is necessary to suppress the formation of these structures.

Conversion Mechanism-Driven Lithium Storage in Sr2CoMoO6 Double Perovskite for High-Performance Anode

The dominance of graphite as the anode material in Lithium-ion batteries (LIBs) is challenged by its inherent limitations. The restricted theoretical capacity of 372 mAh/g impedes its ability to satisfy the escalating demands for high-energy density storage solutions [1-3]. Furthermore, lithium plating during cycling raises serious safety concerns, and graphite exhibits poor capacity retention at high current densities [4]. To address these shortcomings, the development of anode materials with superior capacity, exceptional cycling stability, and enhanced safety characteristics is of prime importance. Conversion reactions present a compelling strategy for achieving significantly higher capacities compared to the conventional intercalation/deintercalation mechanisms employed in commercial LIBs [5-6]. These reduction processes involve the transformation of the electrode material during discharge into metal nanoparticles dispersed within a Li2O matrix. This approach offers a promising avenue to overcome the limitations of traditional intercalation mechanisms. Perovskite frameworks, with their diverse functionalities and unique crystal structures, have emerged as attractive candidates for energy storage applications due to their inherent ability to accommodate a wide range of cations [7]. This structural flexibility allows for the design of materials with properties tailored for specific electrochemical applications. Double perovskites (DPs), a subclass of perovskites with ordered B-site cations, present a particularly promising avenue for exploration as anode materials.This study investigates the electrochemical performance of Sr2CoMoO6 (SCMO), a novel double perovskite synthesized via both solution-combustion and solid-state methods, as a potential high-capacity anode material for LIBs. A systematic half-cell configuration was employed for the evaluation of its anodic behaviour. To gain a deeper understanding of the structure and morphology, a comprehensive suite of advanced characterization techniques, including X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), and transmission electron microscopy (TEM), was utilized.SCMO exhibits exceptional electrochemical performance, demonstrating a superior reversible capacity of 575 mAh/g during the initial discharge cycle in LIBs. Notably, the material showcases remarkable cycling stability, retaining an impressive 540 mAh/g after 250 cycles at a current density of 100 mA/g. This excellent performance is achieved within a broad potential window of 0.01-2.5 V, signifying the versatility of our material for practical battery applications. Furthermore, SCMO demonstrates remarkable rate capability, maintaining stable capacity across a wide range of current densities. This highlights the ability to deliver high power output, a crucial parameter for various portable electronic devices. To gain deeper insights into the underlying lithium storage mechanism, ex situ characterization employing XRD, XPS, SEM, and TEM was performed after cycling. The analyses revealed a conversion-dominated process, where Sr2CoMoO6 undergoes reduction to dispersed CoO and MoO3 nanophases embedded within an electrochemically inactive Li2O matrix. This analysis suggests that the high capacity achieved by SCMO originates from the conversion reaction mechanism. These compelling findings strongly advocate for the strategic design of DPs that exploit conversion mechanisms for lithium storage. This approach offers a promising avenue to significantly enhance the overall electrochemical performance of DP electrodes in LIB applications. By harnessing the unique properties of DPs and optimizing the conversion reaction process, researchers can develop next-generation anode materials with superior capacity, exceptional cycling stability, and improved safety characteristics. This paves the way for the development of high-performance LIBs that can meet the demands of the ever-evolving energy landscape. Figure 1

An Ultrastable Aqueous Ammonium-Ion Battery Using a Covalent Organic Framework Anode.

Aqueous ammonium ion batteries have garnered significant research interest due to their safety and sustainability advantages. However, the development of reliable ammonium-based full batteries with consistent electrochemical performance, particularly in terms of cycling stability, remains challenging. A primary issue stems from the lack of suitable anode materials, as the relatively large NH4 + ions can cause structural damage and material dissolution during battery operation. To address this challenge, an Aza-based covalent organic framework (COF) material is introduced as an anode for aqueous ammonium ion batteries. This material exhibits superior ammonium storage capabilities compared to existing anode materials. It operates effectively within a negative potential range of 0.3 to‒1.0 V versus SCE, achieves high capacity even at elevated current densities (≈74 mAh g-1 at 10 A g-1), and demonstrates exceptional stability, retaining a capacity over 20000 cycles at 1.0 A g-1. Furthermore, by pairing this COF anode with a Prussian blue cathode, an ammonium rocking-chair full battery is developedd that maintains 89% capacity over 20000 cycles at 1.0 A g-1, surpassing all previously reported ammonium ion full batteries. This study offers insights for the design of future anodes for ammonium ion batteries and holds promise for high-energy storage solutions.

Multiple states of two-dimensional turbulence above topography

The recent work of Siegelman & Young (Proc. Natl Acad. Sci. USA, vol. 120, issue 44, 2023, e2308018120) revealed two extreme states reached by the evolution of unforced and weakly damped two-dimensional turbulence above random rough topography, separated by a critical kinetic energy $E_\#$ . The low- and high-energy solutions correspond to topographically locked and roaming vortices, surrounded by non-uniform and homogeneous background potential vorticity (PV), respectively. However, we found that these phenomena are restricted to the particular intermediate length scale where the energy was initially injected into the system. Through simulations initialized by injecting the energy at larger and smaller length scales, we found that the long-term state of topographic turbulence is also dependent on the initial length scale and thus the initial enstrophy. If the initial length scale is comparable to the domain size, the long-term flow field resembles the minimum-enstrophy state proposed by Bretherton & Haidvogel (J. Fluid Mech., vol. 78, issue 1, 1976, pp. 129–154), with very few topographically locked vortices; the long-term enstrophy is quite close to the minimum value, especially when the energy is no larger than $E_\#$ . As the initial length scale becomes smaller, more vortices nucleate and become more mobile; the long-term enstrophy increasingly deviates from the minimum value. Simultaneously, the background PV tends to homogenization, even if the energy is below $E_\#$ . These results complement the phenomenology of topographic turbulence documented by Siegelman & Young, by showing that the minimum-enstrophy and background PV homogenization states can be adequately approached by large- and small-scale initial fields, respectively, with relatively arbitrary energy.

Microstructure and properties of Cu–Ni–Si–Cr alloy fabricated by vacuum-assisted die casting via direct aging

In this study, the Cu−3.18Ni−0.75Si−0.28Cr (wt.%) alloy was fabricated using vacuum-assisted die casting (VADC), and the microstructure and properties of the alloy before and after direct aging treatment were investigated. The synergistic effects of pressure and high cooling rate during the VADC process yield excellent composition uniformity within the alloy, characterized by fine-grained microstructures and the formation of a high-energy metastable supersaturated solid solution. The subsequent direct artificial aging (723 K/6 h) leads to the precipitation of nano-sized δ−Ni2Si phases, thereby enhancing both the mechanical properties and electrical conductivity of the VADC alloy. The alloy exhibited an impressive synergy of the ultimate tensile strength (659 ± 14 MPa), hardness (250.7 ± 3.8 HV), and elongation (21.5 ± 3.6 %), with an excellent conductivity of 32.3 ± 0.4 % IACS. With the considerable potential for industrial applications, the novel fabrication method enables high-efficiency preparation and near-net shape forming of high-performance Cu–Ni–Si–Cr alloy.

Infinitely many solutions for a bi‐nonlocal problem of s(m)‐Kirchhoff‐type without Ambrosetti–Rabinowitz condition

This paper deals with the existence and multiplicity results for a bi‐nonlocal problem without the Ambrosetti–Rabinwitz condition, in the context of variable exponents of Sobolev spaces on compact Riemannian manifolds. Using the mountain pass theorem, we obtain that our problem admits at least nontrivial weak solutions. Also, using the fountain and dual fountain theorems, we obtain the existence of infinitely many nontrivial high or small energy solutions.

Investigation into the impact of charging rates on the stress development within silicon composite electrodes.

Silicon, renowned for its remarkable energy density, has emerged as a focal point in the pursuit of high-energy storage solutions for the next generation. Nevertheless, silicon electrodes are known to undergo significant volume expansion during the insertion of lithium ions, leading to structural deformation and the development of internal stresses, and causing a rapid decline in battery capacity and overall lifespan. To gain deeper insights into the intricacies of charge rate effects, this study employs a combination of in situ measurements and computational modeling to elucidate the cyclic performance of composite silicon electrodes. The findings derived from the established model and curvature measurement system unveil the substantial alterations in stress and deformation as a consequence of varying charge rates. Notably, the active layer experiences compressive forces that diminish as the charge rate decreases. At a charge rate of 0.2, the active layer endures a maximum stress of 89.145 MPa, providing a comprehensive explanation for the observed deterioration in cycling performance at higher charge rates. This study not only establishes a fundamental basis for subsequent stress analyses of silicon electrodes but also lays a solid foundation for further exploration of the impact of charge rates on composite silicon electrodes.

On a class of elliptic equations with critical perturbations in the hyperbolic space

We study the existence and non-existence of positive solutions for the following class of nonlinear elliptic problems in the hyperbolic space − Δ B N u − λ u = a ( x ) u p − 1 + ε u 2 ∗ − 1 in B N , u ∈ H 1 ( B N ) , where B N denotes the hyperbolic space, 2 < p < 2 ∗ : = 2 N N − 2 , if N ⩾ 3 ; 2 < p < + ∞, if N = 2, λ < ( N − 1 ) 2 4 , and 0 < a ∈ L ∞ ( B N ). We first prove the existence of a positive radially symmetric ground-state solution for a ( x ) ≡ 1. Next, we prove that for a ( x ) ⩾ 1, there exists a ground-state solution for ε small. For proof, we employ “conformal change of metric” which allows us to transform the original equation into a singular equation in a ball in R N . Then by carefully analysing the energy level using blow-up arguments, we prove the existence of a ground-state solution. Finally, the case a ( x ) ⩽ 1 is considered where we first show that there is no ground-state solution, and prove the existence of a bound-state solution (high energy solution) for ε small. We employ variational arguments in the spirit of Bahri–Li to prove the existence of high energy-bound-state solutions in the hyperbolic space.

Multiple high energy solutions of a nonlinear Hardy–Sobolev critical elliptic equation arising in astrophysics

In this article, we study the existence and multiplicity of high energy solutions to the problem proposed as a model for the dynamics of galaxies: −Δu+V(x)u=|u|2∗−2u|y|,x=(y,z)∈Rm×Rn−m,where n>4, 2≤m<n, 2∗≔2(n−1)n−2 and potential function V(x):Rn→R. Benefiting from a global compactness result, we show that there exist at least two positive high energy solutions. Our proofs are based on barycenter function, quantitative deformation lemma and Brouwer degree theory.

Enhancing the stability of Li2NiO2 cathode additive with polyborosiloxane coating for high-energy lithium-ion batteries

Li2NiO2 has garnered considerable interest as a Li-excess cathode additive for high-energy lithium-ion batteries (LIBs), attributed to its high irreversible capacity during the initial cycle and an operating voltage comparable with that of commercial cathode materials. However, its integration into practical applications is limited by its suboptimal cycling performance owing to moisture instability and gas evolution. To surmount these obstacles, we developed a hybrid surface coating strategy employing polyborosiloxane (PBS)—a structural derivative of polydimethylsiloxane (PDMS) synthesized with boric acid (H3BO3)—applied to a Li2NiO2 cathode additive. The bi-functional of the PBS layer enhances moisture resistance and ionic conductivity on the Li2NiO2 surface. A hydrophobic, elastic PDMS matrix offers conformal coverage, forestalling adverse moisture-induced side reactions. The introduction of H3BO3 into the PDMS matrix on the Li2NiO2 surface fosters the formation of Li–B–O bonds, thus augmenting the ionic conductivity of the coating. This innovative approach with the PBS layer significantly diminishes the interfacial resistance and improves the cycling performance of Li2NiO2 while preventing substantial structural degradation. In a full-cell configuration incorporating a PBS-coated Li2NiO2 cathode additive with a LiNi0.8Co0.1Mn0.1O2 cathode and a SiOx/Graphite anode, the enhanced energy density and sustained stable cycling performance exceed 300 cycles. This hybrid layer can aid in producing longer-lasting, more efficient LIBs that can fulfill the requirements for use in high-energy storage solutions.

New results concerning a singular biharmonic equations with p-Laplacian and Hardy potential

This paper deals with a singular biharmonic equations with p-Laplacian and Hardy potential. Using Mountain Pass Theorem and Fountain Theorem with Cerami condition, we obtain the existence and multiplicity of sign-changing high-energy solutions under some suitable conditions on the nonlinear term f ( x , u ) . In addition, by applying an abstract critical point theorem of Kajikiya in [A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations. J Funct Anal. 2005;225(2):352–370], a sequence of sign-changing solutions converging to zero for the biharmonic equations with sublinear nonlinearities is also obtained.

High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity

This article deals with the study of the following Kirchhoff–Choquard problem: M∫RN|∇u|p(-Δp)u+V(x)|u|p-2u=∫RNF(u)(y)|x-y|μdyf(u),inRN,u>0,inRN,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\begin{array}{cc} \\displaystyle M\\left( \\, \\int \\limits _{{\\mathbb {R}}^N}|\ abla u|^p\\right) (-\\Delta _p) u + V(x)|u|^{p-2}u = \\left( \\, \\int \\limits _{{\\mathbb {R}}^N}\\frac{F(u)(y)}{|x-y|^{\\mu }}\\,dy \\right) f(u), \\;\\;\ ext {in} \\; {\\mathbb {R}}^N,\\\\ u > 0, \\;\\; \ ext {in} \\; {\\mathbb {R}}^N, \\end{array} \\end{aligned}$$\\end{document}where M models Kirchhoff-type nonlinear term of the form M(t)=a+btθ-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M(t) = a + bt^{\ heta -1}$$\\end{document}, where a,b>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a, b > 0$$\\end{document} are given constants; 1<p<N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<p<N$$\\end{document}, Δp=div(|∇u|p-2∇u)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta _p = \ ext {div}(|\ abla u|^{p-2}\ abla u)$$\\end{document} is the p-Laplacian operator; potential V∈C2(RN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V \\in C^2({\\mathbb {R}}^N)$$\\end{document}; f is monotonic function with suitable growth conditions. We obtain the existence of a positive high energy solution for θ∈1,2N-μN-p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta \\in \\left[ 1, \\frac{2N-\\mu }{N-p}\\right) $$\\end{document} via the Pohožaev manifold and linking theorem. Apart from this, we also studied the radial symmetry of solutions of the associated limit problem.

Existence of high energy solutions for superlinear coupled Klein-Gordons and Born-Infeld equations

In this article, we study the system of Klein-Gordon and Born-Infeld equations $$\displaylines{ -\Delta u +V(x)u-(2\omega+\phi)\phi u =f(x,u), \quad x\in \mathbb{R}^3,\cr \Delta \phi+\beta\Delta_4\phi=4\pi(\omega+\phi)u^2, \quad x\in \mathbb{R}^3, }$$ where \(\Delta_4\phi=\hbox{div}(|\nabla\phi|^2\nabla\phi)$\), \(\omega\) is a positive constant. Assuming that the primitive of \(f(x,u)\) is of 2-superlinear growth in \(u\) at infinity, we prove the existence of multiple solutions using the fountain theorem. Here the potential \(V\) are allowed to be a sign-changing function. For more information see https://ejde.math.txstate.edu/Volumes/2024/18/abstr.html

Existence of Multiple High‐Energy Solutions for a Kind of Superlinear Second‐Order Elliptic Equations

In this paper, we intend to consider infinitely many high energy solutions for a kind of superlinear Klein–Gordon–Maxwell systems. Under some suitable assumptions on the potential function and nonlinearity, by using variational methods and the method of Nehari manifold, we obtain the existence result of infinitely many high energy solutions for this kind of systems, which improves many relative results in the literature.

Infinitely many low- and high-energy solutions for double phase problems with nonstandard growth

The aim of this paper is the study a class of double phase problems with variable exponent. Using the Clark’s theorem and the symmetric mountain pass lemma, we prove the existence of infinitely many small solutions and infinitely many large solutions, respectively.

A Comprehensive Evaluation of Battery Technologies for High-Energy Aqueous Batteries.

Aqueous batteries have garnered significant attention in recent years as a viable alternative to lithium-ion batteries for energy storage, owing to their inherent safety, cost-effectiveness, and environmental sustainability. This study offers a comprehensive review of recent advancements, persistent challenges, and the prospects of aqueous batteries, with a primary focus on energy density compensation of various battery engineering technologies. Additionally, cutting-edge high-energy aqueous battery designs are emphasized as a reference for future endeavors in the pursuit of high-energy storage solutions. Finally, a dual-compatibility battery configuration perspective aimed at concurrently optimizing cycle stability, redox potential, capacity utilization for both anode and cathode materials, as well as the selection of potential electrode candidates, is proposed with the ultimate goal of achieving cell-level energy densities exceeding 400 Wh kg-1.

A study on non-destructive detecting method for carbon particles inside metal structures based on X-ray imaging with contrast agents

The non-destructive detecting of carbon deposits inside metal structures is of great significance for the study of coke accumulating behavior and lifetime assessment of aerospace engines. However, due to the carbon is difficult to be clearly imaged in metal channels under X-rays, there is still a lack of high-resolution and low-cost detecting methods. In this work, firstly, theoretical analysis of X-ray attenuation in graphite and different mediums was conducted. It was found that the linear attenuation coefficient lac of carbon, air and RP-3 fuel are small and similar compared to that of stainless steel matrix material. This explains the difficulty for X-ray visualization of carbon in metal structures. Subsequently, this work proposed a novel approach for X-ray imaging of carbon deposits inside metal structures, utilizing high-density salt solution as contrast agent. The imaging characteristics of different solutions of sodium metatungstate (SMT), ammonium metatungstate (AMT), and sodium iodide (NaI) with different concentrations were compared as experimental contrast agents. The results demonstrated that under the irradiation of high-energy X-rays, the SMT and AMT solutions generated image with significantly higher resolution compared to the traditional medical contrast agent NaI solution. This superiority is attributed to the high density ρ and the large effective atomic number Zeff of metatungstate solutions. Among them, the X-ray absorption intensity of saturated SMT solutions exceeded that of 304 stainless steel, and the imaging contrast index Fct was increased by 124% compared to air. This work provides a feasible method for the non-destructive detecting of carbon deposits in metal structures.

Infinitely many high energy solutions for fourth-order elliptic equations with p-Laplacian in bounded domain

Infinitely many high energy solutions for fourth-order elliptic equations with p-Laplacian in bounded domain

Multiplicity and Stability of the Pohozaev Obstruction for Hardy-Schrödinger Equations with Boundary Singularity

Let Ω \Omega be a smooth bounded domain in R n \mathbb {R}^n ( n ≥ 3 n\geq 3 ) such that 0 ∈ ∂ Ω 0\in \partial \Omega . We consider issues of non-existence, existence, and multiplicity of variational solutions in H 1 , 0 2 ( Ω ) H_{1,0}^2(\Omega ) for the borderline Dirichlet problem, { − Δ u − γ u | x | 2 − h ( x ) u a m p ; = a m p ; | u | 2 ⋆ ( s ) − 2 u | x | s a m p ; in Ω , u a m p ; = a m p ; 0 a m p ; on ∂ Ω ∖ { 0 } , \begin{equation*} \left \{ \begin {array}{llll} -\Delta u-\gamma \frac {u}{|x|^2}- h(x) u &amp;=&amp; \frac {|u|^{2^\star (s)-2}u}{|x|^s} \ \ &amp;\text {in } \Omega ,\\ \hfill u&amp;=&amp;0 &amp;\text {on }\partial \Omega \setminus \{ 0 \} , \end{array} \right . \end{equation*} where 0 &gt; s &gt; 2 0&gt;s&gt;2 , 2 ⋆ ( s ) ≔ 2 ( n − s ) n − 2 {2^\star (s)}≔\frac {2(n-s)}{n-2} , γ ∈ R \gamma \in \mathbb {R} and h ∈ C 0 ( Ω ¯ ) h\in C^0(\overline {\Omega }) . We use sharp blow-up analysis on—possibly high energy—solutions of corresponding subcritical problems to establish, for example, that if γ &gt; n 2 4 − 1 \gamma &gt;\frac {n^2}{4}-1 and the principal curvatures of ∂ Ω \partial \Omega at 0 0 are non-positive but not all of them vanishing, then Equation (E) has an infinite number of high energy (possibly sign-changing) solutions in H 1 , 0 2 ( Ω ) H_{1,0}^2(\Omega ) . This complements results of the first and third authors, who showed in their 2016 article, Hardy-Singular Boundary Mass and Sobolev-Critical Variational Problems, that if γ ≤ n 2 4 − 1 4 \gamma \leq \frac {n^2}{4}-\frac {1}{4} and the mean curvature of ∂ Ω \partial \Omega at 0 0 is negative, then ( E ) (E) has a positive least energy solution. On the other hand, the sharp blow-up analysis also allows us to show that if the mean curvature at 0 0 is nonzero and the mass, when defined, is also nonzero, then there is a surprising stability of regimes where there are no variational positive solutions under C 1 C^1 -perturbations of the potential h h . In particular, and in sharp contrast with the non-singular case (i.e., when γ = s = 0 \gamma =s=0 ), we prove non-existence of such solutions for ( E ) (E) in any dimension, whenever Ω \Omega is star-shaped and h h is close to 0 0 , which include situations not covered by the classical Pohozaev obstruction.