Existence of Solutions for Nonhomogeneous A-Harmonic Equations with Variable Growth. (25th July 2012)

• Record Type: Journal Article
• Authors: Fu, Yongqiang; Guo, Lifeng
• Other Names: Lai Shaoyong Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-07-25
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/421571
• Languages: English
• ISSNs: 1085-3375

Abstract

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 ) .