Uniqueness of positive solutions for singular problems involving the p-Laplacian

Arkady Poliakovsky; Itai Shafrir

doi:10.1090/S0002-9939-05-07290-4

Uniqueness of positive solutions for singular problems involving the p-Laplacian

Arkady Poliakovsky, Itai Shafrir

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9 Scopus citations

Abstract

We study existence and uniqueness of positive eigenfunctions for the singular eigenvalue problem: - Δ_pu - λη(x) u ^p-1/|x|^p = μ u^p-1/|x|^p on a bounded smooth domain Ω ⊂ ℝ^N with zero boundary condition. We also characterize all positive solutions of - Δ_pu = | N-p/p| u ^p-1/|x|^pin ℝ^N \{0}.

Original language	English
Pages (from-to)	2549-2557
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	133
Issue number	9
DOIs	https://doi.org/10.1090/S0002-9939-05-07290-4
State	Published - 1 Sep 2005
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-05-07290-4

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title = "Uniqueness of positive solutions for singular problems involving the p-Laplacian",

abstract = "We study existence and uniqueness of positive eigenfunctions for the singular eigenvalue problem: - Δpu - λη(x) u p-1/|x|p = μ up-1/|x|p on a bounded smooth domain Ω ⊂ ℝN with zero boundary condition. We also characterize all positive solutions of - Δpu = | N-p/p| u p-1/|x|pin ℝN \{0}.",

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AU - Shafrir, Itai

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N2 - We study existence and uniqueness of positive eigenfunctions for the singular eigenvalue problem: - Δpu - λη(x) u p-1/|x|p = μ up-1/|x|p on a bounded smooth domain Ω ⊂ ℝN with zero boundary condition. We also characterize all positive solutions of - Δpu = | N-p/p| u p-1/|x|pin ℝN \{0}.

AB - We study existence and uniqueness of positive eigenfunctions for the singular eigenvalue problem: - Δpu - λη(x) u p-1/|x|p = μ up-1/|x|p on a bounded smooth domain Ω ⊂ ℝN with zero boundary condition. We also characterize all positive solutions of - Δpu = | N-p/p| u p-1/|x|pin ℝN \{0}.

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Uniqueness of positive solutions for singular problems involving the p-Laplacian

Abstract

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