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

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≤p0 are studied. The key ingredient is a special constrained minimization method.