Multiple positive solutions for the one-dimensional singular p-Laplacian

Haishen Lü; Donal O'Regan; Chengkui Zhong

doi:10.1016/S0096-3003(01)00240-5

Multiple positive solutions for the one-dimensional singular p-Laplacian

Haishen Lü
, Donal O'Regan
, Chengkui Zhong

Mathematics

Second Hospital of Lanzhou University

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

44 Citations (Scopus)

Abstract

We consider the following boundary value problem: (φ_p(y′))′ + q(t)f(y) = 0, p > 1, t ∈ [0,1], with y(0) = y(1) = 0, or y(0) = y′(1) = 0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem. An example is also included to illustrate the importance of the result obtained.

Original language	English
Pages (from-to)	407-422
Number of pages	16
Journal	Applied Mathematics and Computation
Volume	133
Issue number	2-3
DOIs	https://doi.org/10.1016/S0096-3003(01)00240-5
Publication status	Published - 15 Dec 2002

Keywords

Boundary value problems
Multiple positive solutions

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10.1016/S0096-3003(01)00240-5

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AU - O'Regan, Donal

AU - Zhong, Chengkui

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N2 - We consider the following boundary value problem: (φp(y′))′ + q(t)f(y) = 0, p > 1, t ∈ [0,1], with y(0) = y(1) = 0, or y(0) = y′(1) = 0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem. An example is also included to illustrate the importance of the result obtained.

AB - We consider the following boundary value problem: (φp(y′))′ + q(t)f(y) = 0, p > 1, t ∈ [0,1], with y(0) = y(1) = 0, or y(0) = y′(1) = 0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem. An example is also included to illustrate the importance of the result obtained.

KW - Boundary value problems

KW - Multiple positive solutions

UR - https://www.scopus.com/pages/publications/0037114103

U2 - 10.1016/S0096-3003(01)00240-5

DO - 10.1016/S0096-3003(01)00240-5

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ER -

Multiple positive solutions for the one-dimensional singular p-Laplacian

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Keywords

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