Infinitely many solutions for a critical p(x)-Kirchhoff equation with Steklov boundary value

Abstract

In this paper, we aim to tackle the questions of existence and multiplicity of solutions of the $ p(x) $-Kirchhoff problem involving critical exponent and the Steklov boundary value. Further, we research the results from the theory of variable exponent Sobolev spaces, the concentration-compactness principle, and the symmetric mountain pass theorem.

Keywords

• variational methods
• critical exponent
• the concentration-compactness principle
• kirchhoff equation
• steklov problem