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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Existence, uniqueness, and stability of oscillations in differential equations with asymmetric nonlinearities


Authors: A. C. Lazer and P. J. McKenna
Journal: Trans. Amer. Math. Soc. 315 (1989), 721-739
MSC: Primary 34A10; Secondary 34C25, 34D05, 70K20, 70K40
MathSciNet review: 979963
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Abstract: We give conditions for the existence, uniqueness, and asymptotic stability of periodic solutions of a second-order differential equation with piecewise linear restoring and $ 2\pi $-periodic forcing where the range of the derivative of the restoring term possibly contains the square of an integer. With suitable restrictions on the restoring and forcing in the undamped case, we give a necessary and sufficient condition.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0979963-1
PII: S 0002-9947(1989)0979963-1
Keywords: Unique periodic solution, continuation argument, implicit function theorem
Article copyright: © Copyright 1989 American Mathematical Society