Almost Periodic Solutions of First-Order Ordinary Differential Equations

Seifedine Kadry, Gennady Alferov, Gennady Ivanov and Artem Sharlay
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Seifedine Kadry: Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Beirut, P.O. Box 11-5020, Lebanon
Gennady Alferov: Saint Petersburg State University, Universitetskaya nab. 7-9, 199034 Saint Petersburg, Russia
Gennady Ivanov: Saint Petersburg State University, Universitetskaya nab. 7-9, 199034 Saint Petersburg, Russia
Artem Sharlay: Saint Petersburg State University, Universitetskaya nab. 7-9, 199034 Saint Petersburg, Russia

Mathematics, 2018, vol. 6, issue 9, 1-21

Abstract: 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.

Keywords: ODE; periodic solutions; upper bounds; lower bounds; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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