Positive solutions to multi-critical elliptic problems

DOI10.1007/s10231-022-01262-2OpenAlexW4293506648MaRDI QIDQ2687959

Xiaohui Yu, Fanqin Liu, Jianfu Yang

Publication date: 7 March 2023

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.10050

zbMATH Keywords

multiple solutionselliptic equationmulti-critical problem

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Elliptic equations and elliptic systems (35Jxx)

Cites Work

• Unnamed Item
• Ground states for a nonlinear elliptic equation involving multiple Hardy-Sobolev critical exponents
• Multiple solutions to a magnetic nonlinear Choquard equation
• On some nonlinear elliptic PDEs with Sobolev-Hardy critical exponents and a Li-Lin open problem
• The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
• On the elliptic problems involving multi-singular inverse square potentials and multi-critical Sobolev-Hardy exponents
• Revisiting an idea of Brézis and Nirenberg
• Positive solutions of some nonlinear elliptic problems in exterior domains
• The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation
• Multiplicity of positive solutions to a \(p\)-Laplacian equation involving critical nonlinearity.
• Minimax theorems
• Classification of solutions to a nonlocal equation with doubly Hardy-Littlewood-Sobolev critical exponents
• Critical growth elliptic problems involving Hardy-Littlewood-Sobolev critical exponent in non-contractible domains
• A nonlinear elliptic PDE with multiple Hardy-Sobolev critical exponents in \(\mathbb{R}^N\)
• The effect of topology on the number of positive solutions of elliptic equation involving Hardy-Littlewood-Sobolev critical exponent
• Multiple positive solutions for a slightly subcritical Choquard problem on bounded domains
• A nonlinear elliptic PDE with two Sobolev-Hardy critical exponents
• Doubly critical problems involving fractional Laplacians in \(\mathbb{R}^N\)
• An elliptic equation with combined critical Sobolev-Hardy terms
• Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• A multiplicity result for a variational problem with lack of compactness
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Existence and multiplicity of positive solutions for nonlinear elliptic problems in exterior domains with “rich” topology
• Remarks on some quasilinear elliptic equations
• Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains