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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Periodic solutions for a class of ordinary differential equations

Author: James R. Ward
Journal: Proc. Amer. Math. Soc. 78 (1980), 350-352
MSC: Primary 34C25
MathSciNet review: 553374
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Abstract: A T-periodic solution to the differential equation $ x'' + cx' + g(x) = f(t) \equiv f(t + T)$ is shown to exist whenever a simple condition on g holds, provided $ c \ne 0$. No assumption is made concerning the growth of g. The condition on g is necessary if g is either an increasing or a decreasing function.

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  • [1] Svatopluk Fučík and Vladimír Lovicar, Periodic solutions of the equation 𝑥^{′′}(𝑡)+𝑔(𝑥(𝑡))=𝑝(𝑡), Časopis Pěst. Mat. 100 (1975), no. 2, 160–175. MR 0385239
  • [2] A. C. Lazer, On Schauder’s fixed point theorem and forced second-order nonlinear oscillations, J. Math. Anal. Appl. 21 (1968), 421–425. MR 0221026
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Keywords: Nonlinear ordinary differential equations, periodic solutions
Article copyright: © Copyright 1980 American Mathematical Society