International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 18, Pages 2871-2882
doi:10.1155/IJMMS.2005.2871

Eigenvalue problems for a quasilinear elliptic equation on ℝN

Marilena N. Poulou and Nikolaos M. Stavrakakis

Department of Mathematics, Faculty of Applied Mathematics and Physics, National Technical University of Athens, Zografou Campus, Athens 15780, Greece

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, lim|x|→+∞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.