Existence of positive solutions to some singular and nonsingular second order boundary value problems

D. O'Regan

doi:10.1016/0022-0396(90)90077-3

Existence of positive solutions to some singular and nonsingular second order boundary value problems

D. O'Regan

Trinity College Dublin

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

30 Citations (Scopus)

Abstract

The topological transversality theorem is employed to study existence of solutions to a variety of singular and nonsingular second order boundary value problems of the form y″ + f(t, y, y′) = 0, 0 < t < 1. Here f may be singular at either t = 0, t = 1, y = 0, and/or y′ = 0. The principal tools are the Arzelà-Ascoli theorem, essential maps, and a priori bounds on solutions.

Original language	English
Pages (from-to)	228-251
Number of pages	24
Journal	Journal of Differential Equations
Volume	84
Issue number	2
DOIs	https://doi.org/10.1016/0022-0396(90)90077-3
Publication status	Published - Apr 1990
Externally published	Yes

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title = "Existence of positive solutions to some singular and nonsingular second order boundary value problems",

abstract = "The topological transversality theorem is employed to study existence of solutions to a variety of singular and nonsingular second order boundary value problems of the form y″ + f(t, y, y′) = 0, 0 < t < 1. Here f may be singular at either t = 0, t = 1, y = 0, and/or y′ = 0. The principal tools are the Arzel{\`a}-Ascoli theorem, essential maps, and a priori bounds on solutions.",

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AB - The topological transversality theorem is employed to study existence of solutions to a variety of singular and nonsingular second order boundary value problems of the form y″ + f(t, y, y′) = 0, 0 < t < 1. Here f may be singular at either t = 0, t = 1, y = 0, and/or y′ = 0. The principal tools are the Arzelà-Ascoli theorem, essential maps, and a priori bounds on solutions.

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Existence of positive solutions to some singular and nonsingular second order boundary value problems

Abstract

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