Results 31 to 40 of about 2,592,777 (103)
Existence of infinitely many solutions for a p-Kirchhoff problem in RN
Boundary Value Problems, 2020 We consider the existence of multiple solutions of the following singular nonlocal elliptic problem: { − M ( ∫ R N | x | − a p | ∇ u | p ) div ( | x | − a p | ∇ u | p − 2 ∇ u ) = h ( x ) | u | r − 2 u + H ( x ) | u | q − 2 u , u ( x ) → 0 as | x | → ∞ ,
Zonghu Xiu, Jing Zhao, Jianyi Chen
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Electronic Journal of Differential EquationsIn this article, we investigate the existence and multiplicity of solutions for a fractional differential equations with p-Laplacian equation at resonance in the \(\psi\)-fractional space \(H^{\alpha, \beta; \psi}_p\).
Jose Vanterler da C. Sousa +2 more
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Multiplicity of Solutions for Nonlocal Elliptic System of (p,q)-Kirchhoff Type
Abstract and Applied Analysis, 2011 This paper is concerned with the following nonlocal elliptic system of (p,q)-Kirchhoff type −[M1(∫Ω|∇u|p)]p−1Δpu=λFu(x,u,v), in Ω, −[M2(∫Ω|∇v|q)]q−1Δqv=λFv(x,u,v), in Ω, u=v=0, on ∂Ω.
Bitao Cheng, Xian Wu, Jun Liu
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Electronic Journal of Differential Equations, 2021 In this article, we consider the existence of ground state positive solutions for nonlinear Schrodinger equations of the fractional (p,q)-Laplacian with Rabinowitz potentials defined in \(R^n\), $$ ( -\Delta ) _p^{s_1}u+( -\Delta ) _q^{s_2}u+V ...
Huilin Lv +2 more
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Brezis–Nirenberg type results for the anisotropic p$p$‐Laplacian
Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.Abstract In this paper, we consider a quasilinear elliptic and critical problem with Dirichlet boundary conditions in presence of the anisotropic p$p$‐Laplacian. The critical exponent is the usual p★$p^{\star }$ such that the embedding W01,p(Ω)⊂Lp★(Ω)$W^{1,p}_{0}(\Omega) \subset L^{p^{\star }}(\Omega)$ is not compact.
Stefano Biagi +3 more
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A generalization of Ekeland's variational principle with applications
Electronic Journal of Differential Equations, 2006 In this paper, we establish a variant of Ekeland's variational principle. This result suggest to introduce a generalization of the famous Palais-Smale condition.
Abdel R. El Amrouss, Najib Tsouli
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Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
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Mathematische Nachrichten, Volume 298, Issue 8, Page 2570-2595, August 2025.Abstract We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators of mixed order. The setting that we introduce is very general and comprises, for instance, the sum of two
Serena Dipierro +3 more
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Infinitely many homoclinic solutions for a class of damped vibration problems
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper, we consider the multiplicity of homoclinic solutions for the following damped vibration problems $$ \ddot{x}(t)+B\dot{x}(t)-A(t)x(t)+H_{x}(t,x(t))=0,$$ where $A(t)\in (\mathbb{R},\mathbb{R}^{N})$ is a symmetric matrix for all $t\in \mathbb{
Huijuan Xu, Shan Jiang, Guanggang Liu
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Infinitely many solutions to critical problems involving the p-Grushin operator
Electronic Journal of Differential EquationsWe consider a critical problem in a bounded domain involving the p-Grushin operator. After a truncation argument, we obtain infinitely many solutions to our problem via Krasnoselskii's genus, extending a previous result of Garcia Azorero and Peral Alonso
Paolo Malanchini +2 more
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