Eigenvalue problems for a quasilinear elliptic equation on â„ N

Marilena N. Poulou and Nikolaos M. Stavrakakis

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-12

Abstract:

We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation − Δ p u = λ g ( x ) | u | p − 2 u , x ∈ ℠N , lim | x | → + ∞ u ( x ) = 0 , where Δ p u = 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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:528657

DOI: 10.1155/IJMMS.2005.2871

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