Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-11T21:41:57.292Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Ambrosseti, A. and Prodi, G.. Analisi Non Lineare (Pisa: Scuola Normale Pisa, 1973).Google Scholar
2Bahri, A. and Rabinowitz, P.. A minimax method for a class of Hamiltonian systems with singular potentials. J. Fund. Anal. 82 (1989), 412–428.CrossRefGoogle Scholar
3del Pino, M. and Manásevich, R.. Infinitely many 2π-periodic solutions for a problem arising in Nonlinear Elasticity. J. Differential Equations (to appear).Google Scholar
4Gaete, S. and Manásevich, R.. Existence of a pair of Periodic Solutions of an O.D.E. generalizing a Problem in Nonlinear Elasticity via Variational Methods. J. Math. Anal. Appl. 123 (1988), 257–271.CrossRefGoogle Scholar
5Lazer, A. C. and Solimini, S.. On Periodic Solutions of Nonlinear Differential Equations with Singularities. Proc. Amer. Math. Soc. 88 (1987), 109–114.Google Scholar
6Solimini, S.. On Forced Dynamical Systems with a Singularity of Repulsive Type. Nonlinear Anal. 14 (1990), 489–500.CrossRefGoogle Scholar