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

Abstract

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