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

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

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.