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

Research output

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 languageEnglish
Article number677
JournalMathematics
Volume7
Issue number8
DOIs
Publication statusPublished - 1 Jan 2019

Fingerprint

Functional Analysis
Periodic Solution
Ordinary differential equation
Periodic Problem
First order differential equation
Estimate
Upper and Lower Bounds
Theorem

Scopus subject areas

  • Mathematics(all)

Cite this

@article{b744aa434ec14f70a41c8e64fdc4be49,
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",
year = "2019",
month = "1",
day = "1",
doi = "10.3390/math7080677",
language = "English",
volume = "7",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "8",

}

A new method to study the periodic solutions of the ordinary differential equations using functional analysis. / Kadry, Seifedine; Alferov, Gennady; Ivanov, Gennady; Korolev, Vladimir; Selitskaya, Ekaterina.

In: Mathematics, Vol. 7, No. 8, 677, 01.01.2019.

Research output

TY - JOUR

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 - 2019/1/1

Y1 - 2019/1/1

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 - http://www.scopus.com/inward/record.url?scp=85070471318&partnerID=8YFLogxK

U2 - 10.3390/math7080677

DO - 10.3390/math7080677

M3 - Article

AN - SCOPUS:85070471318

VL - 7

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 8

M1 - 677

ER -