Existence and multiplicity of positive solutions for singular semipositone p-Laplacian equations

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

doi:10.13025/23835

Existence and multiplicity of positive solutions for singular semipositone p-Laplacian equations

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

Mathematics

Department of Mathematical Sciences

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

11 Citations (Scopus)

Abstract

Positive solutions are obtained for the boundary value problem {- \cf0 i -(|u′|^p-2u′)′ = λf(t, u), t ∈ (0, 1), p > 1 u(0) = u(1) = 0. Here f(t, u) ≥ -M, (M is a positive constant) for (t, u) ∈ [0, 1] × (0, ∞). We will show the existence of two positive solutions by using degree theory together with the upper-lower solution method.

Original language	English
Pages (from-to)	449-475
Number of pages	27
Journal	Canadian Journal of Mathematics
Volume	58
Issue number	3
DOIs	https://doi.org/10.13025/23835 https://doi.org/10.4153/cjm-2006-019-2
Publication status	Published - Jun 2006

Keywords

boundary-value-problems
Degree theory
Externally hosted open access publications with University of Galway authors
One dimensional p-Laplacian
Positive solution
Upper and lower solution

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10.13025/23835Licence: CC BY
10.4153/cjm-2006-019-2

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title = "Existence and multiplicity of positive solutions for singular semipositone p-Laplacian equations",

abstract = "Positive solutions are obtained for the boundary value problem \{- \textbackslash{}cf0 i -(|u′|p-2u′)′ = λf(t, u), t ∈ (0, 1), p > 1 u(0) = u(1) = 0. Here f(t, u) ≥ -M, (M is a positive constant) for (t, u) ∈ [0, 1] {\texttimes} (0, ∞). We will show the existence of two positive solutions by using degree theory together with the upper-lower solution method.",

keywords = "boundary-value-problems, Degree theory, Externally hosted open access publications with University of Galway authors, One dimensional p-Laplacian, Positive solution, Upper and lower solution",

author = "Agarwal, \{Ravi P.\} and Daomin Cao and Haishen L{\"u} and Donald O'Regan",

year = "2006",

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doi = "10.13025/23835",

language = "English",

volume = "58",

pages = "449--475",

journal = "Canadian Journal of Mathematics",

issn = "0008-414X",

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T1 - Existence and multiplicity of positive solutions for singular semipositone p-Laplacian equations

AU - Agarwal, Ravi P.

AU - Cao, Daomin

AU - Lü, Haishen

AU - O'Regan, Donald

PY - 2006/6

Y1 - 2006/6

N2 - Positive solutions are obtained for the boundary value problem {- \cf0 i -(|u′|p-2u′)′ = λf(t, u), t ∈ (0, 1), p > 1 u(0) = u(1) = 0. Here f(t, u) ≥ -M, (M is a positive constant) for (t, u) ∈ [0, 1] × (0, ∞). We will show the existence of two positive solutions by using degree theory together with the upper-lower solution method.

AB - Positive solutions are obtained for the boundary value problem {- \cf0 i -(|u′|p-2u′)′ = λf(t, u), t ∈ (0, 1), p > 1 u(0) = u(1) = 0. Here f(t, u) ≥ -M, (M is a positive constant) for (t, u) ∈ [0, 1] × (0, ∞). We will show the existence of two positive solutions by using degree theory together with the upper-lower solution method.

KW - boundary-value-problems

KW - Degree theory

KW - Externally hosted open access publications with University of Galway authors

KW - One dimensional p-Laplacian

KW - Positive solution

KW - Upper and lower solution

UR - http://hdl.handle.net/10379/8733

UR - https://www.scopus.com/pages/publications/33745251091

U2 - 10.13025/23835

DO - 10.13025/23835

M3 - Article

SN - 0008-414X

VL - 58

SP - 449

EP - 475

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 3

ER -

Existence and multiplicity of positive solutions for singular semipositone p-Laplacian equations

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Keywords

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