Abstract and Applied Analysis
Volume 2010 (2010), Article ID 385048, 12 pages
doi:10.1155/2010/385048
Research Article

Nontrivial Solution for a Nonlocal Elliptic Transmission Problem in Variable Exponent Sobolev Spaces

Bilal Cekic and Rabil A. Mashiyev

Department of Mathematics, Dicle University, 21280 Diyarbakir, Turkey

Received 5 May 2010; Accepted 19 December 2010

Academic Editor: Stephen Clark

Copyright © 2010 Bilal Cekic and Rabil A. Mashiyev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, by means of adequate variational techniques and the theory of the variable exponent Sobolev spaces, we show the existence of nontrivial solution for a transmission problem given by a system of two nonlinear elliptic equations of 𝑝 ( 𝑥 ) -Kirchhoff type with nonstandard growth condition.