Non-Trivial Periodic Solutions for a Class of Second Order Differential Equations with Large Delay

被引：0

作者：

Gomez, Adrian ^{[1
]}

Morales, Nolbert ^{[2
]}

Zamora, Manuel ^{[3
]}

机构：

[1] Univ Bio Bio, Dept Matemat, Grp Invest Sistemas Dinam & Aplicac GISDA, Casilla 5-C, Concepcion, Chile

[2] Univ Catolica Santisima Concepcion, Dept Matemat & Fis Aplicadas, Alonso De Ribera 2850, Concepcion, Chile

[3] Univ Oviedo, Polytech Sch Engn EPI, Dept Math, Campus Viesques, Gijon, Spain

来源：

ACTA APPLICANDAE MATHEMATICAE | 2023年 / 188卷 / 01期

关键词：

Differential delay equation; Periodic solutions; Degree theory; Non-perturbative methods; MONOSTABLE EQUATIONS; TRAVELING FRONTS; STABILITY; MODEL; OSCILLATION; BIFURCATION; UNIQUENESS; EXISTENCE; SYSTEMS; WAVES;

D O I：

10.1007/s10440-023-00613-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a result on the existence of a positive periodic solution for the following class of delay equations theta ''(t)-theta(t)+f(theta(t-r))=0.In particular, we find an infinite family of disjoint intervals having the following property: if the delay is within one of these intervals, then the equation admits a non-trivial and even2r-periodic solution. Furthermore, the length of these intervals is constant and depends on the size of the term |f '(eta)|,where eta is the unique positive equilibrium point of the equation. Consequently, we can find periodic solutions for arbitrarily large delays.

引用

页数：9

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