Periodic solutions for perturbed nonlinear differential equations
HTML articles powered by AMS MathViewer
- by T. G. Proctor
- Proc. Amer. Math. Soc. 24 (1970), 815-819
- DOI: https://doi.org/10.1090/S0002-9939-1970-0255921-0
- PDF | Request permission
Abstract:
The existence of periodic solutions of a periodically perturbed system of nonlinear differential equations is established. The construction of such solutions is proved in a more restricted situation. These results generalize well-known results for perturbed linear differential equations. Examples are given.References
- V. M. Alekseev, An estimate for the perturbations of the solutions of ordinary differential equations, Vestnik Moskov. Univ. Ser. I Mat. Meh. 2 (1961), 28–36 (Russian, with English summary). MR 0125293
- V. M. Alekseev, An estimate for the perturbations of the solutions of ordinary differential equations. II, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1961 (1961), no. 3, 3–10 (Russian, with English summary). MR 0133536
- Jack K. Hale, Oscillations in nonlinear systems, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1963. MR 0150402 L. E. May, Perturbation problems in fully nonlinear systems, Dissertation, North Carolina State University, Raleigh, N. C., 1969.
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 24 (1970), 815-819
- MSC: Primary 34.45
- DOI: https://doi.org/10.1090/S0002-9939-1970-0255921-0
- MathSciNet review: 0255921