Multiplicity of Solutions for the Noncooperative Kirchhoff-Type Variable Exponent Elliptic System with Nonlinear Boundary Conditions

Abstract

Considering the solutions of a class of noncooperative Kirchhoff-type p(x)-Laplacian elliptic systems with nonlinear boundary conditions, we derive a sequence of solutions utilizing both the variational method and limit index theory under certain underlying assumptions. The novelty of this study is that we verify the (PS)c* condition using another method, diverging from the approaches cited in the previous literature.

Keywords

• <i>p</i>(<i>x</i>)-Laplacian
• Kirchhoff problem
• nonlinear boundary conditions
• limit index