Proceedings of the American Mathematical Society

Author(s): M. Cherpion; C. De Coster
Journal: Proc. Amer. Math. Soc. 128 (2000), 1779-1791.
MSC (1991): Primary 34A12, 34B15
Posted: December 8, 1999
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34A12, 34B15

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: 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
Posted: December 8, 1999
Communicated by: Hal L. Smith
Copyright of article: Copyright 2000, American Mathematical Society

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