Periodic solutions for a class of ordinary differential equations
HTML articles powered by AMS MathViewer
- by James R. Ward PDF
- Proc. Amer. Math. Soc. 78 (1980), 350-352 Request permission
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.References
- Svatopluk Fučík and Vladimír Lovicar, Periodic solutions of the equation $x^{^{\prime \prime }}(t)+g(x(t))=p(t)$, Časopis Pěst. Mat. 100 (1975), no. 2, 160–175. MR 0385239
- A. C. Lazer, On Schauder’s fixed point theorem and forced second-order nonlinear oscillations, J. Math. Anal. Appl. 21 (1968), 421–425. MR 221026, DOI 10.1016/0022-247X(68)90225-4
- N. G. Lloyd, Degree theory, Cambridge Tracts in Mathematics, No. 73, Cambridge University Press, Cambridge-New York-Melbourne, 1978. MR 0493564
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 350-352
- MSC: Primary 34C25
- DOI: https://doi.org/10.1090/S0002-9939-1980-0553374-2
- MathSciNet review: 553374