Multiple Solutions for Nonlinear Generalized-Kirchhoff type potential Systems in Unbounded Domains

TL;DR

This paper proves the existence of at least three weak solutions for a class of nonlinear Kirchhoff type potential systems in unbounded domains, using variational methods and critical point theory.

Contribution

It introduces new existence results for multiple solutions of nonlinear Kirchhoff systems with variable exponent operators in unbounded domains.

Findings

Established at least three weak solutions under certain conditions.

Applied variational methods and critical point theory.

Extended results to unbounded domains with variable exponents.

Abstract

In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems in unbounded domains, which involves a general variable exponent elliptic operator. Under some suitable conditions on the nonlinearities, we establish existence of at least three weak solutions for the problem. The proof of our main result uses variational methods and the critical theorem of Bonanno and Marano.