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Periodic solutions for perturbed nonlinear differential equations. II.


Author: T. G. Proctor
Journal: Proc. Amer. Math. Soc. 31 (1972), 219-224
DOI: https://doi.org/10.1090/S0002-9939-1972-0289866-9
MathSciNet review: 0289866
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Abstract | References | Additional Information

Abstract: The existence of periodic solutions of the periodic system $ \dot x = \varepsilon g(t,x,y,\varepsilon ),\dot y = f(t,y) + \varepsilon h(t,x,y,\varepsilon )$ is established for small $ \varepsilon $ when the solution of the initial value problem $ \dot y = f(t,y),y(\tau ) = \gamma $ is known and some algebraic and smoothness conditions are satisfied.


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

  • [1] L. Cesari, Asymptotic behavior and stability problems in ordinary differential equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, N.F., Heft 16, SpringerVerlag, Berlin, 1959. MR 22 #9673. MR 0118904 (22:9673)
  • [2] J. K. Hale, Oscillations in nonlinear systems, McGraw-Hill, New York, 1963. MR 27 #401. MR 0150402 (27:401)
  • [3] T. G. Proctor, Periodic solutions for perturbed nonlinear differential equations, Proc. Amer. Math. Soc. 24 (1970), 815-819. MR 41 #581. MR 0255921 (41:581)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0289866-9
Keywords: Periodic solutions, perturbed nonlinear differential equations, variation of constants, contraction mapping
Article copyright: © Copyright 1972 American Mathematical Society

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