Multiple existence of solutions for semilinear elliptic problems on a domain with a rich topology

DOI10.1016/S0362-546X(96)00084-3zbMath0881.35043OpenAlexW2022225008MaRDI QIDQ4346028

Norimichi Hirano

Publication date: 22 February 1998

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(96)00084-3

zbMATH Keywords

multiplicitypositive solutionstopology of the domain

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Index theory and related fixed-point theorems on manifolds (58J20)

Related Items

A nonlinear elliptic equation with critical exponents: Effect of geometry and topology of the domain ⋮ Multiple existence of sign changing solutions for semilinear elliptic problems on \(\mathbb{R}^N\) ⋮ Multiple existence of solutions for a nonlinear elliptic problem on a Riemannian manifold ⋮ Existence of positive solutions for a semilinear elliptic problem with critical Sobolev and Hardy terms

Cites Work

• Unnamed Item
• Unnamed Item
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• On the existence of multiple, single-peaked solutions for a semilinear Neumann problem
• Infinite dimensional Morse theory and multiple solution problems
• On the existence of positive entire solutions of a semilinear elliptic equation
• Dual variational methods in critical point theory and applications
• Existence and multiplicity of positive solutions for nonlinear elliptic problems in exterior domains with “rich” topology