Nontrivial solutions for an asymptotically linear Delta alpha-Laplace equation

Abstract

In this paper, we study a class of degenerate unperturbed problems. We first investigate some properties of eigenvalues and eigenfunctions for the strongly degenerate elliptic operator and then obtain two existence theorems of nontrivial solutions when the nonlinearity is a function with an asymptotically condition.

Keywords

• asymptotically linear
• saddle point theorem
• strongly degenerate elliptic operator