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Periodic solutions of a second order nonlinear differential equation

Published online by Cambridge University Press:  17 April 2009

Bahman Mehri
Bahman Mehri
Affiliation:
Department of Mathematics, University of California Davis, Davis CA95616, United States of America.
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Abstract

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We consider the following non-linear nonautonomous second order differential equation

where h(x) is continuous, f, p are continuous and periodic with respect to t of period w. Using the Leray-Schauder fixed point technique we prove that the above equation possesses at least one non-trivial periodic solution of period w.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 3 , December 1989 , pp. 357 - 361
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Cesari, L., ‘Functional analysis and periodic solution of nonlinear differential equation’, Contributions to Differential Equations 1 (1963), 149–187.Google Scholar
[2]Reissig, R., ‘On the existence of periodic solutions of certain non-autonomous differential equation’, Ann. Mat. Pura Appl. 85 (1970), 235–240.CrossRefGoogle Scholar
[3]Villari, G., ‘Contirbuti allo studio dell, esistenza di Soluzione periodiche per i Sistemi di equazioni differenziali ardinasie’, Ann. Mat. Pura Appl. 69 (1965), 171–190.CrossRefGoogle Scholar