Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 727398, 15 pages
Research Article

Existence Results for the p(x)-Laplacian with Nonlinear Boundary Condition

Department of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450000, China

Received 28 March 2012; Accepted 8 May 2012

Academic Editors: F. Jauberteau and Y. Tsompanakis

Copyright © 2012 Zhiqiang Wei and Zigao Chen. 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.


By using the variational method, under appropriate assumptions on the perturbation terms 𝑓 ( π‘₯ , 𝑒 ) , 𝑔 ( π‘₯ , 𝑒 ) such that the associated functional satisfies the global minimizer condition and the fountain theorem, respectively, the existence and multiple results for the 𝑝 ( π‘₯ ) -Laplacian with nonlinear boundary condition in bounded domain Ω were studied. The discussion is based on variable exponent Lebesgue and Sobolev spaces.