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

 

A semi-Fredholm principle for periodically forced systems with homogeneous nonlinearities


Authors: A. C. Lazer and P. J. McKenna
Journal: Proc. Amer. Math. Soc. 106 (1989), 119-125
MSC: Primary 34C25; Secondary 58E05, 58F22
MathSciNet review: 942635
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Abstract: We show that if the potential in a second-order Newtonian system of differential equations is positively homogeneous of degree two and positive semidefinite, and if the unforced system has no nontrivial $ T$-periodic solutions $ (T > 0)$, then for any continuous $ T$-periodic forcing, there is at least one $ T$-periodic solution.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0942635-9
PII: S 0002-9939(1989)0942635-9
Keywords: Leray-Schauder continuation method, periodic solution
Article copyright: © Copyright 1989 American Mathematical Society