Next Article in Journal
Optimizing Three-Dimensional Constrained Ordered Weighted Averaging Aggregation Problem with Bounded Variables
Previous Article in Journal
Convergence in Fuzzy Semi-Metric Spaces
Article Menu
Issue 9 (September) cover image

Export Article

Open AccessArticle
Mathematics 2018, 6(9), 171; https://doi.org/10.3390/math6090171

Almost Periodic Solutions of First-Order Ordinary Differential Equations

1
Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Beirut, P.O. Box 11-5020, Lebanon
2
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
Full-Text   |   PDF [290 KB, uploaded 19 September 2018]

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. 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).
SciFeed

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top