On asymptotically linear elliptic problems

TL;DR

This paper establishes the existence of ground state solutions for asymptotically linear elliptic problems, addressing both resonant and non-resonant cases, and extends results to cases with odd nonlinearities.

Contribution

It proves the existence of solutions under minimal regularity assumptions and discusses multiplicity results for odd nonlinearities in asymptotically linear elliptic problems.

Findings

Existence of a signed ground state solution at the mountain pass level.

Analysis of both resonant and non-resonant cases.

Multiplicity results for odd nonlinearities.

Abstract

In this paper we prove the existence of a signed ground state solution in the mountain pass level for a class of asymptotically linear elliptic problems, even when the nonlinearity is just continuous in the second variable. The (strongly) resonant and non-resonant cases are discussed. A multiplicity result is also proved when $f$ is odd with respect to the second variable.