Multiplicity of solutions for a class of nonhomogeneous quasilinear elliptic system with locally symmetric condition in $\mathbb{R}^N$

TL;DR

This paper proves the existence of multiple solutions for a class of nonhomogeneous quasilinear elliptic systems in ^N, using variational methods and iteration techniques under minimal growth assumptions.

Contribution

It introduces a novel approach combining Clark's theorem variant and Moser iteration to establish multiple solutions without global symmetry or growth restrictions.

Findings

Multiple solutions exist under specified conditions.

Solutions are obtained with minimal growth assumptions.

The method applies to systems with small perturbations.

Abstract

This paper is concerned with a class of nonhomogeneous quasilinear elliptic system driven by the locally symmetric potential and the small continuous perturbations in the whole-space $\mathbb{R}^N$. By a variant of Clark's theorem without the global symmetric condition and a Moser's iteration technique, we obtain the existence of multiple solutions when the nonlinear term satisfies some growth conditions only in a circle with center 0 and the perturbation term is any continuous function with a small parameter and no any growth hypothesis.