Existence and multiplicity of nontrivial solutions for double resonance semilinear elliptic problems

Abstract

We consider resonance problems at an arbitrary eigenvalue of the Laplacien. We prove the existence of nontrivial solutions for some semilinear elliptic Dirichlet boundary values problems. We also obtain two nontrivial solutions by using Morse theory.

Keywords

• Variational elliptic problem
• resonance
• critical group
• Morse theory
• minimax method.