Existence of Solutions for Nonhomogeneous A‐Harmonic Equations with Variable Growth
Yongqiang Fu, Lifeng Guo · Abstract and Applied Analysis · 2012
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 of .