## Abstract and Applied Analysis

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

#### Abstract

We study the following nonhomogeneous $A$-harmonic equations: ${d}^{*}A(x,du(x))+B(x,u(x))=0,\mathrm{ }\mathrm{ }x\in \mathrm{\Omega },\mathrm{ }u(x)=0,\mathrm{ }x\in \partial \mathrm{\Omega }$, where $\mathrm{\Omega }\subset {\mathbb{R}}^{n}$ 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 ${\mathrm{𝔎}}_{0}^{1,p(x)}(\mathrm{\Omega },{\mathrm{\Lambda }}^{l-\mathrm{1}})$ of ${W}_{0}^{1,p(x)}(\mathrm{\Omega },{\mathrm{\Lambda }}^{l-\mathrm{1}})$.

#### 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

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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