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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Existence of positive solutions for
singular ordinary differential equations
with nonlinear boundary conditions


Authors: L. E. Bobisud and Donal O'Regan
Journal: Proc. Amer. Math. Soc. 124 (1996), 2081-2087
MSC (1991): Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-96-03615-5
MathSciNet review: 1353379
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the existence of nonnegative solutions of the problem $(py')'/p+\mu qg(x,y)=0$, $\lim _{x\to 0+}py'=0$, $h(y'(1))+y(1)=0$ for a physically motivated class of nonlinearity $h$. The results, which are established using a ``forbidden value'' argument, are new even in the case of linear $h$.


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Additional Information

L. E. Bobisud
Affiliation: Department of Mathematics and Statistics, University of Idaho, Moscow, Idaho 83844–1103
Email: bobisud@uidaho.edu

Donal O'Regan
Affiliation: Department of Mathematics, University College Galway, Galway, Ireland
Email: donal.oregan@ucg.ie

DOI: https://doi.org/10.1090/S0002-9939-96-03615-5
Keywords: Boundary value problems, nonlinear boundary conditions, nonlinear alternative
Received by editor(s): January 15, 1995
Communicated by: Hal L. Smith
Article copyright: © Copyright 1996 American Mathematical Society