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
Department of Mathematics, Faculty of Applied Mathematics and Physics, National Technical University of Athens, Zografou Campus, Athens 15780, Greece
Received 14 December 2004; Revised 18 May 2005
Copyright © 2005 Marilena N. Poulou and Nikolaos M. Stavrakakis. 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
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.