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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On periodic solutions of nonlinear differential equations with singularities


Authors: A. C. Lazer and S. Solimini
Journal: Proc. Amer. Math. Soc. 99 (1987), 109-114
MSC: Primary 34C25
MathSciNet review: 866438
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Abstract: Necessary and sufficient conditions for existence of periodic solutions of differential equations containing singularities are given. Our theorems apply to $ u'' + 1/{u^\alpha } = h\left( t \right) \equiv h\left( {t + T} \right)$ for all $ \alpha > 0$ and to $ u'' - 1/{u^\alpha } = h\left( t \right)$ if $ \alpha \geq 1$, and for this case $ \alpha \geq 1$ is an essential condition.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0866438-7
PII: S 0002-9939(1987)0866438-7
Keywords: Sub- and super-solutions, truncation, resonance
Article copyright: © Copyright 1987 American Mathematical Society