Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable Growth

Abstract EN

We study the following nonhomogeneous A-harmonic equations: d*A(x,du(x))+B(x,u(x))=0, x∈Ω, u(x)=0, x∈∂Ω, where Ω⊂ℝn is a bounded and convex Lipschitz domain, A(x,du(x)) and B(x,u(x)) satisfy some p(x)-growth conditions, respectively.

We obtain the existence of weak solutions for the above equations in subspace ?01,p(x)(Ω,Λl-1) of W01,p(x)(Ω,Λl-1).