On the Eigenvalue Problem for the Hardy-Sobolev Operator with Indefinite Weights
Date
2002-04-02
Authors
Sreenadh, Konijeti
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In this paper we study the eigenvalue problem
-Δpu - α(x) |u|p-2 u = λ|u|p-2u, u ∈ W1,p0 (Ω),
where 1 < p ≤ N, Ω is a bounded domain containing 0 in ℝN, Δp is the p-Laplacean, and α(x) is a function related to Hardy-Sobolev inequality. The weight function V(x) ∈ Ls (Ω) may change sign and has nontrivial positive part. We study the simplicity, isolatedness of the first eigen-value, nodal domain properties. Furthermore we show the existence of a nontrivial curve in the Fučik spectrum.
Description
Keywords
p-Laplcean, Hardy-Sobolev operator, Fucik spectrum, Indefinite weight
Citation
Sreenadh, K. (2002). On the eigenvalue problem for the Hardy-Sobolev operator with indefinite weights. <i>Electronic Journal of Differential Equations, 2002</i>(33), pp. 1-12.
Rights
Attribution 4.0 International