Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable Growth. (25th July 2012) - Fu, Yongqiang; Guo, Lifeng
Abstract : We study the following nonhomogeneous A -harmonic equations: d * A ( x, d u ( x ) ) + B ( x, u ( x ) ) = 0,       x ∈ Ω,    u ( x ) = 0,    x ∈ ∂ Ω, where Ω ⊂ ℝ n is a bounded and convex Lipschitz domain, A ( x, d u ( 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 𝔎 0 1, p ( x ) ( Ω, Λ l - 1 ) of W 0 1, p ( x ) ( Ω, Λ l - 1 ) .