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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Existence of solutions
for first order singular problems


Authors: M. Cherpion and C. De Coster
Journal: Proc. Amer. Math. Soc. 128 (2000), 1779-1791
MSC (1991): Primary 34A12, 34B15
Published electronically: December 8, 1999
MathSciNet review: 1694454
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Abstract: We develop the lower and upper solutions method for first order initial value problems as well as for first order periodic problems in case the nonlinearity presents singularities. More precisely we prove that if we have a lower solution $\alpha$ and an upper solution $\beta$ of these problems, which are not necessarily continuous nor ordered, we have a solution wedged between $\min\{\alpha,\beta\}$ and $\max\{\alpha,\beta\}$.


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Additional Information

M. Cherpion
Affiliation: Université Catholique de Louvain, Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron 2, 1348 Louvain-La-Neuve, Belgique
Email: cherpion@amm.ucl.ac.be

C. De Coster
Affiliation: Université du Littoral - Côte d’Opale, Centre Universitaire de la Mi-Voix, 50 Rue F. Buisson, B.P. 699, 62228 Calais Cédex, France
Email: decoster@lma.univ-littoral.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05515-X
PII: S 0002-9939(99)05515-X
Keywords: Singular first order initial value problem, singular first order periodic BVP, lower and upper solutions method
Received by editor(s): July 24, 1998
Published electronically: December 8, 1999
Communicated by: Hal L. Smith
Article copyright: © Copyright 2000 American Mathematical Society