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Mathematics 2018, 6(9), 171;

Almost Periodic Solutions of First-Order Ordinary Differential Equations

Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Beirut, P.O. Box 11-5020, Lebanon
Saint Petersburg State University, Universitetskaya nab. 7-9, 199034 Saint Petersburg, Russia
Author to whom correspondence should be addressed.
Received: 22 August 2018 / Revised: 12 September 2018 / Accepted: 14 September 2018 / Published: 17 September 2018
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Approaches to estimate the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determination for both upper and lower bounds for these solutions are found. The existence and stability of almost periodic problems are studied. The novelty of this paper lies in the fact that the use of apparatus derivatives allows for the reduction of restrictions on the degree of smoothness of the right parts. In our work, regarding the number of periodic solutions of equations first order, we don’t require a high degree of smoothness and no restriction on the smoothness of the second derivative of the Schwartz equation. We have all of these restrictions lifted. Our new form presented also emphasizes this novelty. View Full-Text
Keywords: ODE; periodic solutions; upper bounds; lower bounds; stability ODE; periodic solutions; upper bounds; lower bounds; stability
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Kadry, S.; Alferov, G.; Ivanov, G.; Sharlay, A. Almost Periodic Solutions of First-Order Ordinary Differential Equations. Mathematics 2018, 6, 171.

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