Boundary Value Problems
Volume 2007 (2007), Article ID 16407, 8 pages
Research Article

Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations

Zuodong Yang and Bing Xu

Institute of Mathematics, School of Mathematics and Computer Sciences, Nanjing Normal University, Jiangsu Nanjing 210097, China

Received 29 June 2006; Accepted 17 October 2006

Academic Editor: Shujie Li

Copyright © 2007 Zuodong Yang and Bing Xu. 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.


We consider the problem div(|u|p2u)=a(x)(um+λun), xN, N3, where 0<m<p1<n,a(x)0, a(x) is not identically zero. Under the condition that a(x) satisfies (H), we show that there exists λ0>0 such that the above-mentioned equation admits at least one solution for all λ(0,λ0). This extends the results of Laplace equation to the case of p-Laplace equation.