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

Yongqiang Fu and Lifeng Guo

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: 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 𝔎01,p(x)(Ω,Λl-1) of W01,p(x)(Ω,Λl-1).

Date: 2012
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https://doi.org/10.1155/2012/421571

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:421571

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