Eigenvalue problems for a quasilinear elliptic equation on ℝN

Abstract

We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation -Δpu = λg(x) u p-2u, x ∈ ℝN, limx rarr;+∞u(x) = 0, where Δpu = div( ∇u p-2∇u) is the p-Laplacian operator and the weight function g(x), being bounded, changes sign and is negative and away from zero at infinity.