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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Existence of periodic solutions of nonlinear differential equations


Author: R. Kannan
Journal: Trans. Amer. Math. Soc. 217 (1976), 225-236
MSC: Primary 34C25
DOI: https://doi.org/10.1090/S0002-9947-1976-0397091-4
MathSciNet review: 0397091
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Abstract: The nonlinear differential equation $ x'' = f(t,x(t))$, f being $ 2\pi $-periodic in t, is considered for the existence of $ 2\pi $-periodic solutions. The equation is reduced to an equivalent system of two Hammerstein equations. The case of nonlinear perturbation at resonance is also discussed.


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DOI: https://doi.org/10.1090/S0002-9947-1976-0397091-4
Article copyright: © Copyright 1976 American Mathematical Society