On the Eigenvalue Problem for the Hardy-Sobolev Operator with Indefinite Weights
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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.
CitationSreenadh, K. (2002). On the eigenvalue problem for the Hardy-Sobolev operator with indefinite weights. Electronic Journal of Differential Equations, 2002(33), pp. 1-12.
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