Existence of Solutions for NonhomogeneousA-Harmonic Equations with Variable Growth

Abstract

We study the following nonhomogeneousA-harmonic equations:d*A(x,du(x))+B(x,u(x))=0,    x∈Ω,  u(x)=0,  x∈∂Ω, whereΩ⊂ℝnis a bounded and convex Lipschitz domain,A(x,du(x))andB(x,u(x))satisfy somep(x)-growth conditions, respectively. We obtain the existence of weak solutions for the above equations in subspace𝔎01,p(x)(Ω,Λl-1)ofW01,p(x)(Ω,Λl-1).