Existence results for a nonlinear elliptic transmission problem of $p(x)$-Kirchhoff type

Abstract

In this article, we establish the existence of weak solutions for a nonlinear transmission problem involving nonlocal coefficients of $p(x)$-Kirchhoff type in two different domains, which are connected by a nonlinear transmission condition at their interface. We get our results by means of the monotone operator theory and the $(S_{+})$ mapping theory; the weak formulation takes place in suitable variable exponent Sobolev spaces.

Keywords

• nonlinear transmission problem
• p(x)-laplacian
• monotone operator