Existence of Multiple Solutions for Second Order Boundary Value Problems

Henderson, J and Thompson, H. B. (2000) Existence of Multiple Solutions for Second Order Boundary Value Problems. Journal of Differential Equations, 166 2: 443-454. doi:10.1006/jdeq.2000.3797

Author Henderson, J
Thompson, H. B.
Title Existence of Multiple Solutions for Second Order Boundary Value Problems
Journal name Journal of Differential Equations   Check publisher's open access policy
ISSN 0022-0396
Publication date 2000-09-20
Year available 2002
Sub-type Article (original research)
DOI 10.1006/jdeq.2000.3797
Open Access Status Not yet assessed
Volume 166
Issue 2
Start page 443
End page 454
Total pages 12
Editor J.K. Hale
Place of publication USA
Publisher Academic Press
Language eng
Subject 230107 Differential, Difference and Integral Equations
780101 Mathematical sciences
Abstract We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.
Keyword Schauder degree
two point boundary value problems
Bernstein–Nagumo growth condition
lower solutions
upper solutions
multiple solutions
Q-Index Code C1
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Physical Sciences Publications
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Citation counts: TR Web of Science Citation Count  Cited 82 times in Thomson Reuters Web of Science Article | Citations
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Created: Thu, 31 May 2007, 22:02:08 EST by Mrs Leith Woodall on behalf of School of Mathematics & Physics