Almost Periodic Solutions of First-Order Ordinary Differential Equations

Seifedine Kadry, Gennady Alferov, Gennady Ivanov, Artem Sharlay

Research output

2 Citations (Scopus)

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.

Original languageEnglish
Article number171
Number of pages21
JournalMathematics
Volume6
Issue number9
DOIs
Publication statusPublished - Sep 2018

Scopus subject areas

  • Mathematics(all)

Cite this

Kadry, Seifedine ; Alferov, Gennady ; Ivanov, Gennady ; Sharlay, Artem. / Almost Periodic Solutions of First-Order Ordinary Differential Equations. In: Mathematics. 2018 ; Vol. 6, No. 9.
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Almost Periodic Solutions of First-Order Ordinary Differential Equations. / Kadry, Seifedine; Alferov, Gennady; Ivanov, Gennady; Sharlay, Artem.

In: Mathematics, Vol. 6, No. 9, 171, 09.2018.

Research output

TY - JOUR

T1 - Almost Periodic Solutions of First-Order Ordinary Differential Equations

AU - Kadry, Seifedine

AU - Alferov, Gennady

AU - Ivanov, Gennady

AU - Sharlay, Artem

PY - 2018/9

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N2 - 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.

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KW - periodic solutions

KW - upper bounds

KW - lower bounds

KW - stability

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