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Periodic solutions of ordinary differential equations with one-sided growth restrictions

Published online by Cambridge University Press:  14 November 2011

J. Mawhin  and
W. Walter
J. Mawhin
Affiliation:
Institut Mathématique, Université de Louvain, Belgium
W. Walter
Affiliation:
Mathematisches Institut I, Universität Karlsruhe, West Germany
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Synopsis

The existence of periodic solutions is proved for first order vector ordinary and functional differential equations when the right-hand side satisfies a one-sided growth restriction of Wintner type together with some conditions of asymptotic nature. Special cases in the line of Landesman-Lazer and of Winston are explicited.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 95 - 106
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Coppel, W. A.. Stability and Asymptotic Behavior of Differential Equations (Boston: Heath, 1965).Google Scholar
2Deimling, K.. Nichtlineare Gleichungen und Abbildungsgrade (Berlin: Springer, 1974).CrossRefGoogle Scholar
3Gaines, R. E. and Mawhin, J.. Coincidence Degree and Non-linear Differential Equations. Lecture Notes in Mathematics 568 (Berlin: Springer, 1977).Google Scholar
4Gossez, J. P. and Figueiredo, D. G. de. Perturbation non-linéaire d'un problème elliptique linéaire près de sa première valeur propre. C.R. Acad. Sci. Paris Sér. A 284 (1977), 163–166.Google Scholar
5Krasnosel'skii, M. A.. The Operator of Translation along the Trajectories of Differential Equations (Providence, R.I.: Amer. Math. Soc., 1968).Google Scholar
6Landesman, E. M. and Lazer, A. C.. Non-linear perturbations of linear elliptic boundary value problems at resonance. J. Math. Mech. 19 (1970), 609–632.Google Scholar
7Mawhin, J.. Periodic solutions of non-linear functional differential equations. J. Differential Equations 10 (1971), 240–261.CrossRefGoogle Scholar
8Mawhin, J.. Equivalence theorems for non-linear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces. J. Differential Equations 12 (1972), 610–636.CrossRefGoogle Scholar
9Mawhin, J.. Boundary value problems at resonance for vector second order non-linear ordinary differential equations. In Proceedings Equadiff IV, Prague, August 1977, to appear.Google Scholar
10Rouche, N. and Mawhin, J.. Equations différentielles ordinaires, 2 (Paris: Masson, 1973).Google Scholar
11Winston, E.. The existence of periodic solutions of perturbed periodic systems. SLAM J. Appl. Math. 21 (1971), 95–103.CrossRefGoogle Scholar