Solutions for a quasilinear elliptic p⃗(x)${\vec{p}(x)}$‐Kirchhoff type problem with weight and nonlinear Robin boundary conditions

Abstract

This paper deals with the existence and multiplicity of weak solutions to a class of quasilinear elliptic ⃗ 𝑝(𝑥)-Kirchhoff type problems with weight and a nonlinearRobin boundary condition such aswhere Ω is a smooth bounded domain. Under suitable conditions on the data, we show the existence and multiplicity of weak solutions by means of a variational approach in the framework of anisotropic Sobolev spaces with variable exponents.