The effect of topology on the number of positive solutions of elliptic equation involving Hardy-Littlewood-Sobolev critical exponent

DOI10.12775/TMNA.2019.068zbMath1441.49008arXiv1902.07437OpenAlexW2983567613MaRDI QIDQ2178782

Divya Goel

Publication date: 11 May 2020

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.07437

zbMATH Keywords

critical exponentLjusternik-Schnirelman theoryChoquard equation

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Nonlinear elliptic equations (35J60) Existence of solutions for minimax problems (49J35) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Positive solutions to PDEs (35B09)

Related Items

Existence of positive solutions for a class of fractional Choquard equation in exterior domain ⋮ Multiple solutions to multi-critical Schrödinger equations ⋮ Positive solutions to multi-critical elliptic problems ⋮ Multiple solutions to Choquard equation in exterior domain

Cites Work

• Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity
• Multiple solutions to a magnetic nonlinear Choquard equation
• Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain
• On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents
• Multiplicity of positive solutions to a \(p\)--\(q\)-Laplacian equation involving critical nonlinearity
• The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
• Multiple positive solutions for a Schrödinger-Poisson-Slater system
• The effect of the domain topology on the number of solutions of fractional Laplace problems
• The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation
• Doubly nonlocal system with Hardy-Littlewood-Sobolev critical nonlinearity
• Multiplicity of positive solutions to a \(p\)-Laplacian equation involving critical nonlinearity.
• Minimax theorems
• Positive and sign changing solutions to a nonlinear Choquard equation
• Multiple positive solutions for a slightly subcritical Choquard problem on bounded domains
• Regularity results on a class of doubly nonlocal problems
• Coron problem for nonlocal equations involving Choquard nonlinearity
• Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• A multiplicity result for a variational problem with lack of compactness
• A Note on an Equation with Critical Exponent
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Critical points and nonlinear variational problems
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Positive solutions for the p-Laplacian: application of the fibrering method
• Existence of solutions for critical Choquard equations via the concentration-compactness method
• Existence of groundstates for a class of nonlinear Choquard equations
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