The Multiplicity of Nontrivial Solutions for a New p x -Kirchhoff-Type Elliptic Problem

Abstract

In the paper, we study the existence of weak solutions for a class of new nonlocal problems involving a $p\left(x\right)$ -Laplacian operator. By using Ekeland’s variational principle and mountain pass theorem, we prove that the new $p\left(x\right)$ -Kirchhoff problem has at least two nontrivial weak solutions.