A new method to study the periodic solutions of the ordinary differential equations using functional analysis

Seifedine Kadry; Gennady Alferov; Gennady Ivanov; Vladimir Korolev; Ekaterina Selitskaya

doi:10.3390/math7080677

A new method to study the periodic solutions of the ordinary differential equations using functional analysis

Seifedine Kadry
, Gennady Alferov
, Gennady Ivanov
, Vladimir Korolev
, Ekaterina Selitskaya

Beirut Arab University
St. Petersburg State University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.

Original language	English
Article number	677
Journal	Mathematics
Volume	7
Issue number	8
DOIs	https://doi.org/10.3390/math7080677
State	Published - 2019
Externally published	Yes

Keywords

Derived number
Dini-Holder derivatives
Non-smooth analysis
Periodic solutions

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10.3390/math7080677

Cite this

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title = "A new method to study the periodic solutions of the ordinary differential equations using functional analysis",

abstract = "In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.",

keywords = "Derived number, Dini-Holder derivatives, Non-smooth analysis, Periodic solutions",

author = "Seifedine Kadry and Gennady Alferov and Gennady Ivanov and Vladimir Korolev and Ekaterina Selitskaya",

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T1 - A new method to study the periodic solutions of the ordinary differential equations using functional analysis

AU - Kadry, Seifedine

AU - Alferov, Gennady

AU - Ivanov, Gennady

AU - Korolev, Vladimir

AU - Selitskaya, Ekaterina

PY - 2019

Y1 - 2019

N2 - In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.

AB - In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.

KW - Derived number

KW - Dini-Holder derivatives

KW - Non-smooth analysis

KW - Periodic solutions

UR - https://www.scopus.com/pages/publications/85070471318

U2 - 10.3390/math7080677

DO - 10.3390/math7080677

M3 - Article

AN - SCOPUS:85070471318

SN - 2227-7390

VL - 7

JO - Mathematics

JF - Mathematics

IS - 8

M1 - 677

ER -

A new method to study the periodic solutions of the ordinary differential equations using functional analysis

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Keywords

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