One solution for Steklov problems involving nonstandard growth conditions of Kirchhoff type

Abstract

We explore the presence of at least one weak solution for a nonlocal problem of the $ p(x) $ p(x)-Kirchhoff type, featuring Steklov boundary values within variable exponent Sobolev spaces arising in the nonlinear elasticity theory and the theory of electrorheological fluids. Our methodology relies on variational techniques. Additionally, we provide an illustrative example to showcase the practical application of our principal findings.