Indefinite Weight Research Articles

Loss of body weight is dose-dependently associated with reductions in symptoms of hip osteoarthritis.

While weight loss is recommended for managing hip osteoarthritis (OA), most evidence comes from knee OA studies, limiting its applicability to hip OA. This study addresses this gap by examining the effects of weight loss on hip OA symptoms. A retrospective audit of routinely collected healthcare data from participants enrolled in the Osteoarthritis Healthy Weight for Life (OAHWFL) program, designed for individuals with knee or hip OA. In total, 1714 adults with hip OA were selected from the OAHWFL program; 1408 completed the initial 18-week weight loss phase, while 306 did not complete it. After 18 weeks, participants transitioned to an indefinite weight maintenance phase. Percentage change in body weight from baseline at 18 weeks. Changes in the five subscales of the Hip Disability and Osteoarthritis Outcome Score (HOOS) (Pain, Activity Limitations in Daily Living, Stiffness and Range of Motion, Sports and Recreation Function, and Hip-related Quality of Life) from baseline to 18 weeks. Linear regression, adjusted for sex and baseline values of age, weight, and respective HOOS scores, assessed the relationship between percentage weight change (analyzed as both a continuous variable and in categories: ≤2.5%, >2.5-5.0%, >5.0-7.5%, >7.5-10%, and >10% of baseline weight) and changes in all five HOOS subscales. At baseline, participants had a mean age of 65.14 years, 70% were female, and 78% were individuals with obesity (Body Mass Index ≥30 kg/m2). A statistically significant dose-response relationship was observed between weight loss and improvements in all HOOS subscales, with the greatest improvement in the Hip-related Quality of Life subscale (14.42 points, 31.14%) for >10% weight loss. Our findings suggest that weight loss is associated with reduced symptoms of hip OA, supporting weight loss as an effective treatment strategy for hip OA.

On a Class of p(z)-Biharmonic Kirchhoff Type Problems with Indefinite Weight and No-Flow Boundary Condition

On a Class of p(z)-Biharmonic Kirchhoff Type Problems with Indefinite Weight and No-Flow Boundary Condition

A singular perturbation result for a class of periodic-parabolic BVPs

Abstract In this article, we obtain a very sharp version of some singular perturbation results going back to Dancer and Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag, Berlin, 1990, pp. 12–19] and Daners and López-Gómez [The singular perturbation problem for the periodic-parabolic logistic equation with indefinite weight functions, J. Dynam. Differential Equations 6 (1994), 659–670] valid for a general class of semilinear periodic-parabolic problems of logistic type under general boundary conditions of mixed type. The results of Dancer and Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag, Berlin, 1990, pp. 12–19] and [The singular perturbation problem for the periodic-parabolic logistic equation with indefinite weight functions, J. Dynam. Differential Equations 6 (1994), 659–670] were found, respectively, for Neumann and Dirichlet boundary conditions with L = − Δ {\mathfrak{L}}=-\Delta . In this article, L {\mathfrak{L}} stands for a general second-order elliptic operator.

Triple weak solution for p(x)-Laplacian like problem involving no flux boundary condition

Abstract In this paper, we consider a class of p ⁢ ( x ) {p(x)} -Laplacian like problems with indefinite weight involving no flux boundary condition. Using variational techniques and the critical point theorem of Bonanno and Marano [4], we prove the existence of at least three weak solutions to the problem in Sobolev variable exponent spaces.

Asymptotic properties of an optimal principal Dirichlet eigenvalue arising in population dynamics

We consider a shape optimization problem related to the persistence threshold for a biological species, the unknown shape corresponding to the zone of the habitat which is favorable to the population. Analytically, this translates in the minimization of a weighted eigenvalue of the Dirichlet Laplacian, with respect to a bang-bang indefinite weight. For such problem, we provide a full description of the singularly perturbed regime in which the volume of the favorable zone vanishes, with particular attention to the interplay between its location and shape.First, we show that the optimal favorable zone shrinks to a connected, nearly spherical set, in C1,1 sense, which aims at maximizing its distance from the lethal boundary. Secondly, we show that the spherical asymmetry of the optimal favorable zone decays exponentially, with respect to a negative power of its volume, in the C1,α sense, for every α<1. This latter property is based on sharp quantitative asymmetry estimates for the optimization of a weighted eigenvalue problem on the full space, of independent interest.

Positive solutions for parametric equations with unbalanced growth and indefinite perturbation

We consider a nonlinear Dirichlet problem driven by the double phase operator. The reaction has the combined effects of parametric concave term and of an indefinite convex one (“concave-convex” problem with indefinite weight). Using the Nehari method we prove the existence of two bounded, positive ground state solutions.

On a class of fractional p( x, y)−Kirchhoff type problems with indefinite weight

This paper is concerned with a class of fractional \(p(x,y)-\)Kirchhoff type problems with Dirichlet boundary data along with indefinite weight of the following form \begin{equation*} \left\lbrace\begin{array}{ll} M\left(\int_{Q}\frac{1}{p(x,y)}\frac{|u(x)-u(y)|^{p(x,y)}}{|x-y|^{N+sp(x,y)}}\,dx\,dy\right)\\ (-\triangle_{p(x)})^s+|u(x)|^{q(x)-2}u(x) &amp; \\ =\lambda V(x)|u(x)|^{r(x)-2}u(x)&amp; \text{in }\Omega,\\ u=0, &amp; \text{in }\mathbb{R}^N\Omega. \end{array}\right. \end{equation*} By means of direct variational approach and Ekeland’s variational principle, we investigate the existence of nontrivial weak solutions for the above problem in case of the competition between the growth rates of functions \(p\) and \(r\) involved in above problem, this fact is essential in describing the set of eigenvalues of this problem.

Global structure of positive solutions for p-Laplacian Neumann problem with indefinite weight

Global structure of positive solutions for p-Laplacian Neumann problem with indefinite weight

Existence and bifurcation of periodic solutions to the Lp-Minkowski problem with indefinite weight

This paper is devoted to the existence and bifurcation of positive periodic solutions for Lp-Minkowski problem with indefinite weight. We provide new sufficient conditions for the existence of at least one positive periodic solution. The main tools are Leray-Schauder alternative principle and a global continuation theorem by Manásevich-Mawhin. Using the numerical bifurcation theory, we study the dynamic behaviors of periodic solutions in the cases of indefinite and positive weight, where the weight term is a simple sinusoidal function. In the positive weight case, the multiplicity of positive periodic solutions is detected for the first time in the Lp-Minkowski problem, which is generated by a saddle-node bifurcation.

Multiplicity result for a (p(x),q(x))-Laplacian-like system with indefinite weights

Abstract Under some suitable conditions, we show that at least three weak solutions exist for a system of differential equations involving the ( p ⁢ ( x ) , q ⁢ ( x ) ) {(p(x),q(x))} Laplacian-like with indefinite weights. The proof is related to the Bonanno–Marano critical theorem (Appl. Anal. 89 (2010), 1–10).

Triple solutions for a Leray-Lions $ p(x) $-biharmonic operator involving Hardy potential and indefinite weight

&lt;p&gt;Existence and multiplicity of three weak solutions for a Leray-Lions $ p(x) $-biharmonic problem involving Hardy potential and indefinite weight were proved. Our main tools combined variational methods and some critical theorems.&lt;/p&gt;

Subharmonic bouncing solutions for a class of sublinear impact oscillators with indefinite weight

Subharmonic bouncing solutions for a class of sublinear impact oscillators with indefinite weight

Positive solutions for the periodic-parabolic problem with large diffusion

&lt;p&gt;In this paper, we study the positive solutions of the periodic-parabolic logistic equation with indefinite weight function and nonhomogeneous diffusion coefficient. By employing sufficient conditions to guarantee negative principal eigenvalue, we obtain the existence, uniqueness, and stability of the positive periodic solutions. Moreover, we prove that the positive periodic solution tends to the unique positive solution of the corresponding non-autonomous logistic equation when the diffusion rate is large.&lt;/p&gt;

Non‐autonomous double phase eigenvalue problems with indefinite weight and lack of compactness

AbstractIn this paper, we consider eigenvalues to the following double phase problem with unbalanced growth and indefinite weight, where , , , , and is an indefinite sign weight which may admit non‐trivial positive and negative parts. Here, is the ‐Laplacian operator and is the weighted ‐Laplace operator defined by . The problem can be degenerate, in the sense that the infimum of in may be zero. Our main results distinguish between the cases and . In the first case, we establish the existence of a continuous family of eigenvalues, starting from the principal frequency of a suitable single phase eigenvalue problem. In the latter case, we prove the existence of a discrete family of positive eigenvalues, which diverges to infinity.

Time-inconsistent stochastic linear-quadratic control problem with indefinite control weight costs

Time-inconsistent stochastic linear-quadratic control problem with indefinite control weight costs

Positive Solutions for Third-Order Boundary Value Problems with Indefinite Weight

Positive Solutions for Third-Order Boundary Value Problems with Indefinite Weight

Existence and multiplicity of solutions for α(x)-Kirchhoff Equation with indefinite weights

Existence and multiplicity of solutions for α(x)-Kirchhoff Equation with indefinite weights

Multiplicity of solutions for a non-local problem with indefinite weights

In this manuscript, we show that at least three weak solutions exist for a non-local -biharmonic problem. The variational method and the critical theorem of Bonanno and Marano (Appl. Anal. 89 (2010), 1–10) are used to prove our main result.

On the fractional P–Q laplace operator with weights

We exploit the existence and non-existence of positive solutions to the eigenvalue problem driven by the nonhomogeneous fractional p &q Laplacian operator with indefinite weights ( − Δ p ) α u + ( − Δ q ) β u = λ [ a | u | p − 2 u + b | u | q − 2 u ] in Ω , where Ω ⊆ R N is a smooth bounded domain that has been extended by zero. We further show the existence of a continuous family of eigenvalues in the case Ω = R N and b ≡ 0 a.e. Our approach relies strongly on variational Analysis, in which the Mountain pass theorem plays the key role. Due to the lack of spatial compactness and the embedding W α , p ( R N ) ↪ W β , q ( R N ) in R N , we employ the concentration-compactness principle of P.L. Lions [The concentration-compactness principle in the calculus of variations. The limit case. II, Rev Mat Iberoamericana. 1985;1(2):45–121]. to overcome the difficulty. Our paper can be considered as a counterpart to the important works [Alves et al. Existence, multiplicity and concentration for a class of fractional p &q Laplacian problems in R N , Commun Pure Appl Anal, 2019;18(4):2009–2045], [Benci et al. An eigenvalue problem for a quasilinear elliptic field equation. J Differ Equ, 2002;184(2):299–320], [Bobkov et al. On positive solutions for ( p , q ) -Laplace equations with two parameters, Calc Var Partial Differ Equ, 2015;54(3):3277–3301], [Colasuonno and Squassina. Eigenvalues for double phase variational integrals, Ann Mat Pura Appl (4), 2016;195(6):1917–1956], [Papageorgiou et al. Positive solutions for nonlinear Neumann problems with singular terms and convection, J Math Pures Appl (9), 2020;136:1–21], [Papageorgiou et al. Ground state and nodal solutions for a class of double phase problems, Z Angew Math Phys, 2020;71:1–15], and may have further applications to deal with other problems.

Maximum and anti-maximum principle for the fractional p-Laplacian with indefinite weights

We establish some non-resonance results and maximum and anti-maximum principles for the following quasilinear non local problem involving the fractional p-Laplacian operator perturbed by an indefinite potential{(−Δp)su+V|u|p−2u=λm|u|p−2u+f in Ω,u=0 in RN﹨Ω. Here p∈(1,+∞), s∈(0,1), V and m are indefinite and sign-changing functions of Lr(Ω) with r>max⁡{N,Nsp}; f∈Lr(Ω) is such that f≥0 and f≢0 in the regular bounded domain Ω⊂RN.