International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2005 / Article

Open Access

Volume 2005 |Article ID 528657 | https://doi.org/10.1155/IJMMS.2005.2871

Marilena N. Poulou, Nikolaos M. Stavrakakis, "Eigenvalue problems for a quasilinear elliptic equation on N", International Journal of Mathematics and Mathematical Sciences, vol. 2005, Article ID 528657, 12 pages, 2005. https://doi.org/10.1155/IJMMS.2005.2871

Eigenvalue problems for a quasilinear elliptic equation on N

Received14 Dec 2004
Revised18 May 2005

Abstract

We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation Δpu=λg(x)|u|p2u, xN, lim|x|+u(x)=0, where Δpu=div(|u|p2u) is the p-Laplacian operator and the weight function g(x), being bounded, changes sign and is negative and away from zero at infinity.

Copyright © 2005 Hindawi Publishing Corporation. 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.


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