Existence theorems for the one-dimensional singular p-Laplacian equation with a nonlinear boundary condition

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

doi:10.13025/23439

Existence theorems for the one-dimensional singular p-Laplacian equation with a nonlinear boundary condition

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

Mathematics

Hohai University
Department of Mathematical Sciences

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

16 Citations (Scopus)

Abstract

In this paper, general existence theorems are presented for the singular equation -(φ_p(y′))′ = q(t)f(t, y), 0 < t < 1, y(0) = 0, Ψ(y(1)) + y′(1) = 0. Throughout, our nonlinearity is allowed to change sign. The singularity may occur at y = 0, t = 0 and t = 1. In addition, Ψ may be nonlinear.

Original language	English
Pages (from-to)	188-210
Number of pages	23
Journal	Journal of Computational and Applied Mathematics
Volume	182
Issue number	1
DOIs	https://doi.org/10.13025/23439 https://doi.org/10.1016/j.cam.2004.10.022
Publication status	Published - 1 Oct 2005

Keywords

membrane response
multiple positive solutions
One-dimensional p-Laplacian
Positive solution
Upper and lower solution

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10.13025/23439Licence: CC BY
10.1016/j.cam.2004.10.022

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abstract = "In this paper, general existence theorems are presented for the singular equation -(φp(y′))′ = q(t)f(t, y), 0 < t < 1, y(0) = 0, Ψ(y(1)) + y′(1) = 0. Throughout, our nonlinearity is allowed to change sign. The singularity may occur at y = 0, t = 0 and t = 1. In addition, Ψ may be nonlinear.",

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AU - O'Regan, Donald

AU - Agarwal, Ravi P.

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N2 - In this paper, general existence theorems are presented for the singular equation -(φp(y′))′ = q(t)f(t, y), 0 < t < 1, y(0) = 0, Ψ(y(1)) + y′(1) = 0. Throughout, our nonlinearity is allowed to change sign. The singularity may occur at y = 0, t = 0 and t = 1. In addition, Ψ may be nonlinear.

AB - In this paper, general existence theorems are presented for the singular equation -(φp(y′))′ = q(t)f(t, y), 0 < t < 1, y(0) = 0, Ψ(y(1)) + y′(1) = 0. Throughout, our nonlinearity is allowed to change sign. The singularity may occur at y = 0, t = 0 and t = 1. In addition, Ψ may be nonlinear.

KW - membrane response

KW - multiple positive solutions

KW - One-dimensional p-Laplacian

KW - Positive solution

KW - Upper and lower solution

UR - http://hdl.handle.net/10379/9453

UR - https://www.scopus.com/pages/publications/19644361852

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EP - 210

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Existence theorems for the one-dimensional singular p-Laplacian equation with a nonlinear boundary condition

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Keywords

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