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Periodic solutions of forced Liénard equations with jumping nonlinearities under nonuniform conditions*

Published online by Cambridge University Press:  14 November 2011

R. Iannacci ,
M.N. Nkashama ,
P. Omari  and
F. Zanolin
R. Iannacci
Affiliation:
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università “La Sapienza”, Via A. Scarpa 10, 00161 Roma, Italy
M.N. Nkashama
Affiliation:
Department of Mathematical Sciences, Memphis State University, Memphis, Tennessee 38152, U.S.A.
P. Omari
Affiliation:
Dipartimento di Scienze Matematiche, Università, P.le Europa 1, 34100 Trieste, Italy
F. Zanolin
Affiliation:
Dipartimento di Matematica ed Informatica, Università, Via Zanon 6, 33100 Udine, Italy
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Synopsis

This paper is devoted to the existence of periodic solutions for the scalar forced Lienard differential equation

The key assumptions relate the asymptotic behaviour as x →± ∞of g(t; x)/x to the “critical values” of the positively 1-homogeneous problem

No condition on f, except continuity, is assumed. Our approach is based on Leray–Schauder degree techniques and a priori estimates.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 3-4 , 1988 , pp. 183 - 198
Copyright
Copyright © Royal Society of Edinburgh 1988

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