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Limit-periodic solutions of integro-differential equations in a critical case

Limit-periodic solutions of integro-differential equations in a critical case We consider equations with nonlinear terms representable by power series in the variable and functionals in integral form. The equation depends on a small exponentially limitperiodic perturbation, i.e., on a function that exponentially tends to a periodic function as the independent variable increases. In the Lyapunov critical case of one zero root, we prove the existence of a family of exponentially limit-periodic solutions of the equation in the form of power series in the small parameter and arbitrary initial values of the noncritical variables. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Limit-periodic solutions of integro-differential equations in a critical case

Differential Equations , Volume 53 (9) – Oct 14, 2017

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References (23)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266117090099
Publisher site
See Article on Publisher Site

Abstract

We consider equations with nonlinear terms representable by power series in the variable and functionals in integral form. The equation depends on a small exponentially limitperiodic perturbation, i.e., on a function that exponentially tends to a periodic function as the independent variable increases. In the Lyapunov critical case of one zero root, we prove the existence of a family of exponentially limit-periodic solutions of the equation in the form of power series in the small parameter and arbitrary initial values of the noncritical variables.

Journal

Differential EquationsSpringer Journals

Published: Oct 14, 2017

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