Boundary Value Problems
Volume 2009 (2009), Article ID 185319, 19 pages
doi:10.1155/2009/185319
Research Article

A Class of p-q-Laplacian Type Equation with Potentials Eigenvalue Problem in RN

Mingzhu Wu1 and Zuodong Yang1,2

1School of Mathematics Science, Institute of Mathematics, Nanjing Normal University, Jiangsu, Nanjing 210097, China
2College of Zhongbei, Nanjing Normal University, Jiangsu, Nanjing 210046, China

Received 20 October 2009; Accepted 6 December 2009

Academic Editor: Wenming Zou

Copyright © 2009 Mingzhu Wu and Zuodong Yang. 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

The nonlinear elliptic eigenvalue problem −div(|∇u|p−2∇u)−div(|∇u|q−2∇u)+λa(x)|u|p−2u+λb(x)|u|q−2u=f(x,u),u∈W1,p∩W1,q(RN), where 2≤q≤p<N and a(x)∈LN/p(RN),b(x)∈LN/q(RN),a(x),b(x)>0 are studied. The key ingredient is a special constrained minimization method.