Nontrivial solutions for nonlinear elliptic problems via Morse theory

Abstract

We prove the existence of nontrivial solutions for perturbations of p-Laplacian. Our approach combine minimax arguments and Morse Theory, under the conditions on the behaviors of the perturbed function $f(x,t)$ or its primitive $F(x,t)$ near infinity and near zero.

Keywords

• Minimax method
• p-Laplacian
• resonance elliptic equation
• critical group
• Morse theory.