Periodic solutions for perturbed nonlinear differential equations
Author:
T. G. Proctor
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
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Abstract | References | Similar Articles | Additional Information
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.
- 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.
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Additional Information
Keywords:
Periodic solutions,
perturbed nonlinear differential equations,
Alekseev formula,
variation of constants,
existence of periodic solutions,
construction of periodic solutions,
Schauder fixed point theorem
Article copyright:
© Copyright 1970
American Mathematical Society