Singular Nonlinearity Research Articles

Multiplicity of solutions for p-Laplacian Kirchhoff problems with singular nonlinearity

Multiplicity of solutions for <i>p</i>-Laplacian Kirchhoff problems with singular nonlinearity

Fractional Sobolev space: Study of Kirchhoff-Schrödinger systems with singular nonlinearity

This study extensively investigates a specific category of Kirchhoff-Schrödinger systems in fractional Sobolev space with Dirichlet boundary conditions. The main focus is on exploring the existence and multiplicity of non-negative solutions. The non-linearity of the problem generally exhibits singularity. By employing minimization arguments involving the Nehari manifold and a variational approach, we establish the existence and multiplicity of positive solutions for our problem with respect to the parameters \(\eta\) and \(\zeta\) in suitable fractional Sobolev spaces. Our key findings are novel and contribute significantly to the literature on coupled systems of Kirchhoff-Schrödinger system with Dirichlet boundary conditions.

Existence of Positive Solutions for Singular Difference Equations with Nonlinear Boundary Conditions

In this paper, we delve into a discrete nonlinear singular semipositone problem, characterized by a nonlinear boundary condition. The nonlinearity, given by f(u)−auα with α&gt;0, exhibits a singularity at u=0 and tends towards −∞ as u approaches 0+. By constructing some suitable auxiliary problems, the difficulty that arises from the singularity and semipositone of nonlinearity and the lack of a maximum principle is overcome. Subsequently, employing the Krasnosel’skii fixed-point theorem, we determine the parameter range that ensures the existence of at least one positive solution and the emergence of at least two positive solutions. Furthermore, based on our existence results, one can obtain the symmetry of the solutions after adding some symmetric conditions on the given functions by using a standard argument.

The combined effects of two singular nonlinearities in some degenerate elliptic equations

The combined effects of two singular nonlinearities in some degenerate elliptic equations

On subelliptic equations on stratified Lie groups driven by singular nonlinearity and weak L 1 data

On subelliptic equations on stratified Lie groups driven by singular nonlinearity and weak L 1 data

Existence result for a Steklov problem involving a singular nonlinearity and variable exponents

Abstract In this paper, we use the variational method to study some singular Steklov-type problem with variable exponents. More precisely, we use the min-max method in order to prove the existence of a solution to such a problem.

Existence and regularity results of parabolic problems with convection term and singular nonlinearity

In this work, we investigate the influence of the convection term and the singular lower order term on the existence and regularity of solutions to the following parabolic problem: \begin{cases}\frac{\partial u}{\partial t}-\operatorname{div}(M(x,t)\nabla u) =-\operatorname{div}(uE(x,t))+\frac{f}{u^{\theta}}&amp;\text{in }\Omega\times(0,T),\\ u(x,t)=0&amp;\text{on }\partial \Omega\times (0,T),\\ u(x,0)=u_{0}(x)&amp;\text{in }\Omega,\end{cases} where \theta&gt;0 , \Omega\subset \mathbb{R}^{N}\ (N&gt;2) is a bounded smooth domain with 0\in \Omega , and f\in L^{m}(\Omega\times (0,T)) with m\geq 1 is a non-negative function. The function u_{0} is a non-negative function that belongs to the space L^{\infty}(\Omega) such that \forall \omega\subset\subset \Omega,\ \exists c_{\omega}&gt;0,\quad u_{0}\geq c_{\omega}\text{ in }\omega. The main idea of this research explains the combined impact of the convection term and the singular lower order term on the existence and regularity of a solution to the above problem.

Periodic fractional Ambrosetti–Prodi for one-dimensional problem with drift

We prove Ambrosetti–Prodi type results for periodic solutions of some one-dimensional nonlinear problems that can have drift term whose principal operator is the fractional Laplacian of order s∈(0,1). We establish conditions for the existence and nonexistence of solutions of those problems. The proofs of the existence results are based on the sub-supersolution method combined with topological degree type arguments. We also obtain a priori bounds in order to get multiplicity results. We also prove that the solutions are C1,α under some regularity assumptions in the nonlinearities, that is, the solutions of the mentioned equations are classical. We finish the work obtaining Ambrosetti-Prodi-type results for a problem with singular nonlinearities.

Generalized Schrödinger–Bopp–Podolsky type system with singular nonlinearity

In this paper we establish the existence, non-existence and multiplicity of solutions for a class of generalized Schrödinger–Bopp–Podolsky system with singular nonlinearity. The main techniques we use are some results on critical point theory for non-differentiable functionals and the sub-supersolution method.

Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity

Existence and multiplicity of positive solutions for a critical fractional Laplacian equation with singular nonlinearity

Nonlinear Degenerate Parabolic Equations with a Singular Nonlinearity

Nonlinear Degenerate Parabolic Equations with a Singular Nonlinearity

Multiple solutions for a fractional $p$-Kirchhoff system with singular nonlinearity

Multiple solutions for a fractional $p$-Kirchhoff system with singular nonlinearity

带有混合奇异项和测度项的分数阶&lt;i&gt;p&lt;/i&gt;-Laplace方程解的存在性问题

带有混合奇异项和测度项的分数阶&lt;i&gt;p&lt;/i&gt;-Laplace方程解的存在性问题

Existence and uniqueness for anisotropic quasilinear elliptic equations involving singular nonlinearities

Existence and uniqueness for anisotropic quasilinear elliptic equations involving singular nonlinearities

Initial value problems for fractional p-Laplacian equations with singularity

&lt;abstract&gt;&lt;p&gt;We have studied initial value problems for Caputo fractional differential equations with singular nonlinearities involving the p-Laplacian operator. We have given a precise mathematical analysis of the equivalence of the fractional differential equations and Volterra integral equations studied in this paper. A theorem for the global existence of the solution was proven. In addition, an example was given at the end of the article as an application of the results found in this paper.&lt;/p&gt;&lt;/abstract&gt;

Global vs Blow-Up Solutions and Optimal Threshold for Hyperbolic ODEs with Possibly Singular Nonlinearities

We consider a hyperbolic ordinary differential equation perturbed by a nonlinearity which can be singular at a point and in particular this includes MEMS type equations. We first study qualitative properties of the solution to the stationary problem. Then, for small value of the perturbation parameter as well as initial value, we establish the existence of a global solution by means of the Lyapunov function and we show that the omega limit set consists of a solution to the stationary problem. For strong perturbations or large initial values, we show that the solution blows up. Finally, we discuss the relationship between upper bounds of the perturbation parameter for the existence of time-dependent and stationary solutions, for which we establish an optimal threshold.

Mixed local and nonlocal elliptic equation with singular and critical Choquard nonlinearity

In this article, we study a class of elliptic problems involving both local and nonlocal operators with different orders and a singular nonlinearity in combination with critical Hartree type nonlinearity (see problem ( P λ ) below). Using variational methods together with the critical point theory of nonsmooth analysis, we show the existence, the regularity and the multiplicity of weak solutions with respect to the parameter λ.

Dirichlet Problems for Fractional Laplace Equations with Singular Nonlinearity

Dirichlet Problems for Fractional Laplace Equations with Singular Nonlinearity

Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation

Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation

On the regularity theory for mixed anisotropic and nonlocal p-Laplace equations and its applications to singular problems

Abstract We establish existence results for a class of mixed anisotropic and nonlocal p-Laplace equations with singular nonlinearities. We consider both constant and variable singular exponents. Our argument is based on an approximation method. To this end, we also discuss the necessary regularity properties of weak solutions of the associated non-singular problems. More precisely, we obtain local boundedness of subsolutions, the Harnack inequality for solutions and the weak Harnack inequality for supersolutions.