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 | References | Similar Articles | Additional Information

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 -periodic solutions , then for any continuous -periodic forcing, there is at least one -periodic solution.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0942635-9

Keywords:
Leray-Schauder continuation method,
periodic solution

Article copyright:
© Copyright 1989
American Mathematical Society