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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: 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 [Enhancements On Off] (What's this?)

  • [1] V. M. Alekseev, An estimate for the perturbations of the solutions of ordinary differential equations. I, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1961, no. 2, 28-36. (Russian) MR 23 #A2596. MR 0125293 (23:A2596)
  • [2] -, An estimate for the perturbations of the solutions of ordinary differential equations. II, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1961, no. 3, 3-10. (Russian) MR 24 #A3367; MR 25, p. 1242. MR 0133536 (24:A3367)
  • [3] J. K. Hale, Oscillations in nonlinear systems, McGraw-Hill, New York, 1963. MR 27 #401. MR 0150402 (27:401)
  • [4] L. E. May, Perturbation problems in fully nonlinear systems, Dissertation, North Carolina State University, Raleigh, N. C., 1969.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0255921-0
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

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