Amann-Zehnder type results for p-Laplace problems

TL;DR

This paper proves the existence of solutions for certain quasilinear elliptic equations involving p-Laplace operators using Morse theory and critical groups, advancing mathematical understanding of these nonlinear problems.

Contribution

It introduces a novel approach combining Morse theory and critical groups to establish solution existence for p-Laplace related equations.

Findings

Existence of nontrivial solutions proved.

Applicable to equations with p-linear growth nonlinearities.

Utilizes advanced Morse theory techniques.

Abstract

The existence of a nontrivial solution is proved for a class of quasilinear elliptic equations involving, as principal part, either the p-Laplace operator or the operator related to the p-area functional, and a nonlinearity with p-linear growth at infinity. To this aim, Morse theory techniques are combined with critical groups estimates.