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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Periodic solutions for perturbed nonlinear differential equations. II.

Author: T. G. Proctor
Journal: Proc. Amer. Math. Soc. 31 (1972), 219-224
MathSciNet review: 0289866
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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.

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Keywords: Periodic solutions, perturbed nonlinear differential equations, variation of constants, contraction mapping
Article copyright: © Copyright 1972 American Mathematical Society