Ground and bound state solutions for quasilinear elliptic systems including singular nonlinearities and indefinite potentials

TL;DR

This paper proves the existence of bound and ground state solutions for complex quasilinear elliptic systems with singular nonlinearities and indefinite potentials, using Nehari methods and fibering map analysis.

Contribution

It introduces a novel approach to handle nonsingular and singular nonlinearities with indefinite potentials without relying on the Ambrosetti-Rabinowitz condition.

Findings

Existence of bound and ground state solutions established.

Multiplicity of semi-trivial solutions demonstrated.

Analysis applicable to both singular and nonsingular cases.

Abstract

It is established existence of bound and ground state solutions for quasilinear elliptic systems driven by (\phi 1, \phi 2)-Laplacian operator. The main feature here is to consider quasilinear elliptic systems involving both nonsingular nonlinearities combined with indefinite potentials and singular cases perturbed by superlinear and subcritical couple terms. These prevent us to use arguments based on Ambrosetti-Rabinowitz condition and variational methods for differentiable functionals. By exploring the Nehari method and doing a fine analysis on the fibering map associated, we get estimates that allow us unify the arguments to show multiplicity of semi-trivial solutions in both cases.