Existence and Nonexistence for a Singular Boundary Value Problem

L. E. Bobisud; D. O'Regan; W. D. Royalty

doi:10.1080/00036818808839765

Existence and Nonexistence for a Singular Boundary Value Problem

L. E. Bobisud
, D. O'Regan
, W. D. Royalty

University of Idaho

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

27 Citations (Scopus)

Abstract

Existence of positive solutions of the two-point boundary value problem y” = λ²f(x,y),y(0) = a > 0, y(1) = b ≥ 0 is studied, where λ² > 0 and [formula omitted] but [formula omitted]. It is shown that positive solutions exist provided λ² is sufficiently small but that no positive solutions exist for λ² large.

Original language	English
Pages (from-to)	245-256
Number of pages	12
Journal	Applicable Analysis
Volume	28
Issue number	4
DOIs	https://doi.org/10.1080/00036818808839765
Publication status	Published - 1 Jan 1988
Externally published	Yes

Keywords

boundary value problems
Existence
nonexistence
nonlinear
positive solutions
reaction-diffusion

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10.1080/00036818808839765

Cite this

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abstract = "Existence of positive solutions of the two-point boundary value problem y” = λ2f(x,y),y(0) = a > 0, y(1) = b ≥ 0 is studied, where λ2 > 0 and [formula omitted] but [formula omitted]. It is shown that positive solutions exist provided λ2 is sufficiently small but that no positive solutions exist for λ2 large.",

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AU - Bobisud, L. E.

AU - O'Regan, D.

AU - Royalty, W. D.

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Y1 - 1988/1/1

N2 - Existence of positive solutions of the two-point boundary value problem y” = λ2f(x,y),y(0) = a > 0, y(1) = b ≥ 0 is studied, where λ2 > 0 and [formula omitted] but [formula omitted]. It is shown that positive solutions exist provided λ2 is sufficiently small but that no positive solutions exist for λ2 large.

AB - Existence of positive solutions of the two-point boundary value problem y” = λ2f(x,y),y(0) = a > 0, y(1) = b ≥ 0 is studied, where λ2 > 0 and [formula omitted] but [formula omitted]. It is shown that positive solutions exist provided λ2 is sufficiently small but that no positive solutions exist for λ2 large.

KW - boundary value problems

KW - Existence

KW - nonexistence

KW - nonlinear

KW - positive solutions

KW - reaction-diffusion

UR - https://www.scopus.com/pages/publications/84963462032

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DO - 10.1080/00036818808839765

M3 - Article

AN - SCOPUS:84963462032

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VL - 28

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JF - Applicable Analysis

IS - 4

ER -

Existence and Nonexistence for a Singular Boundary Value Problem

Abstract

Keywords

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