Abstract and Applied Analysis

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

Yongqiang Fu and Lifeng Guo

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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 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 ) .

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 421571, 26 pages.

Dates
First available in Project Euclid: 4 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365099934

Digital Object Identifier
doi:10.1155/2012/421571

Mathematical Reviews number (MathSciNet)
MR2955023

Zentralblatt MATH identifier
1252.35142

Citation

Fu, Yongqiang; Guo, Lifeng. Existence of Solutions for Nonhomogeneous A -Harmonic Equations with Variable Growth. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 421571, 26 pages. doi:10.1155/2012/421571. https://projecteuclid.org/euclid.aaa/1365099934


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