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T-periodic solutions for some second order differential equations with singularities*

Published online by Cambridge University Press:  14 November 2011

Manuel del Pino ,
Raúl Manásevich  and
Alberto Montero
Manuel del Pino
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.
Raúl Manásevich
Affiliation:
Departamento de Matemáticas, F.C.F.M. U. de Chile, Casilla 170, Correo 3, Santiago, Chile
Alberto Montero
Affiliation:
Departamento de Matemáticas, F.C.F.M. U. de Chile, Casilla 170, Correo 3, Santiago, Chile
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Synopsis

We study the existence of T-periodic positive solutions of the equation

where f(t, .) has a singularity of repulsive type near the origin. Under the assumption that f(t, x) lies between two lines of positive slope for large and positive x, we find a non-resonance condition which predicts the existence of one T-periodic solution.

Our main result gives a Fredholm alternative-like result for the existence of T-periodic positive solutions for

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 120 , Issue 3-4 , 1992 , pp. 231 - 243
Copyright
Copyright © Royal Society of Edinburgh 1992

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