Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 496417, 16 pages
doi:10.1155/2011/496417
Research Article

Existence of Solutions for a Nonlinear Elliptic Equation with General Flux Term

Hee Chul Pak

Department of Applied Mathematics, Dankook University, Cheonan, Chungnam 330-714, Republic of Korea

Received 25 September 2010; Revised 29 January 2011; Accepted 27 February 2011

Academic Editor: D. R. Sahu

Copyright © 2011 Hee Chul Pak. 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

We prove the existence of solutions for an elliptic partial differential equation having more general flux term than either 𝑝 -Laplacian or flux term of the Leray-Lions type conditions: − ∑ 𝑛 𝑗 = 1 ( 𝜕 / 𝜕 𝑥 𝑗 ) ( 𝛼 ( | 𝑢 𝑥 𝑗 | ) / 𝑢 𝑥 𝑗 ) = 𝑓 . Brouwer's fixed point theorem is one of the fundamental tools of the proof.