The Existence of Solutions to the NonhomogeneousA-Harmonic Equations with Variable Exponent

Abstract

We first discuss the existence and uniqueness of weak solution for the obstacle problem of the nonhomogeneousA-harmonic equation with variable exponent, and then we obtain the existence of the solutions of the equationd⋆A(x,dω)=B(x,dω)in the weighted variable exponent Sobolev spaceWdp(x)(Ω,Λl,μ).