Eigenvalues and the one-dimensional p-laplacian

Ravi P. Agarwal; Haishen Lü; Donal O'Regan

doi:10.1006/jmaa.2001.7742

Eigenvalues and the one-dimensional p-laplacian

Ravi P. Agarwal
, Haishen Lü
, Donal O'Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

118 Citations (Scopus)

Abstract

We consider the boundary value problem (φ_p(u′))′ + λF(t,u) =0, with p > 1, t ∈(0, 1), u(0) = u(1) =0, and with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for λ such that, for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition, the existence of two positive solutions for λ in an appropriate interval is also discussed.

Original language	English
Pages (from-to)	383-400
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	266
Issue number	2
DOIs	https://doi.org/10.1006/jmaa.2001.7742
Publication status	Published - 15 Feb 2002

Keywords

Boundary value problems
Positive solutions

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10.1006/jmaa.2001.7742

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T1 - Eigenvalues and the one-dimensional p-laplacian

AU - Agarwal, Ravi P.

AU - Lü, Haishen

AU - O'Regan, Donal

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N2 - We consider the boundary value problem (φp(u′))′ + λF(t,u) =0, with p > 1, t ∈(0, 1), u(0) = u(1) =0, and with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for λ such that, for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition, the existence of two positive solutions for λ in an appropriate interval is also discussed.

AB - We consider the boundary value problem (φp(u′))′ + λF(t,u) =0, with p > 1, t ∈(0, 1), u(0) = u(1) =0, and with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for λ such that, for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition, the existence of two positive solutions for λ in an appropriate interval is also discussed.

KW - Boundary value problems

KW - Positive solutions

UR - https://www.scopus.com/pages/publications/0037084478

U2 - 10.1006/jmaa.2001.7742

DO - 10.1006/jmaa.2001.7742

M3 - Article

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VL - 266

SP - 383

EP - 400

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Eigenvalues and the one-dimensional p-laplacian

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Keywords

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