Ground state solutions for the asymptotically periodic Schr\"odinger-Poisson systems with $p$-Laplacian

TL;DR

This paper investigates the existence of ground state solutions for asymptotically periodic Schr"odinger-Poisson systems involving p-Laplacian and q-Laplacian operators, extending previous results through a variational approach.

Contribution

It introduces a variational method to establish ground state solutions for coupled Schr"odinger-Poisson systems with p-Laplacian and q-Laplacian, including cases with critical growth nonlinearities.

Findings

Established existence of ground state solutions

Extended results to critical growth nonlinearities

Applied variational methods to asymptotically periodic systems

Abstract

In this paper we study the existence of ground state solutions for the asymptotically periodic Schr\"odinger-Poisson systems which are coupled by a Schr\"odinger equation of $p$-Laplacian and a Poisson equation of $q$-Laplacian. The method relies on a variational approach and the case of the nonlinearity exhibits a critical growth is also considered. Some results in the literature are extended.