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Periodic solutions of perturbed conservative systems


Author: James R. Ward
Journal: Proc. Amer. Math. Soc. 72 (1978), 281-285
MSC: Primary 34C25; Secondary 47H15
DOI: https://doi.org/10.1090/S0002-9939-1978-0507323-4
MathSciNet review: 507323
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Abstract: The existence of $ 2\pi $-periodic solutions to the system $ x'' +$   grad$ \; G(x) = p(t,x)$, p being $ 2\pi $-periodic in t, is established under conditions at infinity on the Hessian matrix of G. The condition used is weaker than earlier known conditions of a similar nature.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0507323-4
Keywords: Periodic solutions, boundary value problems, nonlinear system of ordinary differential equations, Hilbert space methods
Article copyright: © Copyright 1978 American Mathematical Society

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