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

共 50 条

[1] Non-Trivial Periodic Solutions for a Class of Second Order Differential Equations with Large Delay
Adrian Gomez
Nolbert Morales
Manuel Zamora
Acta Applicandae Mathematicae, 2023, 188
[2] PERIODIC SOLUTIONS FOR A CLASS OF SECOND-ORDER DIFFERENTIAL DELAY EQUATIONS
Wu, Xuan
Xiao, Huafeng
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2021, 20 (12) : 4253 - 4269
[3] Periodic solutions for a class of second order differential equations
Wang, Weibing
Luo, Yan
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2013, (41) : 1 - 10
[4] Periodic solutions for a class of second order delay differential systems
Meng, Qiong
Ding, Juntang
BOUNDARY VALUE PROBLEMS, 2016, : 1 - 12
[5] Emergence of non-trivial solutions from trivial solutions in reaction-diffusion equations for pattern formation
Zhao, Xinyue Evelyn
Hao, Wenrui
MATHEMATICAL BIOSCIENCES, 2024, 374
[6] Multiple periodic solutions for a class of second order differential equations
Yang, XJ
APPLIED MATHEMATICS LETTERS, 2005, 18 (01) : 91 - 99
[7] On the existence of periodic solutions of third order delay differential equations
Erdur, Sultan
Tunc, Cemil
COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2023, 11 (02): : 319 - 331
[8] Periodic solutions to a class of distributed delay differential equations via variational methods
Xiao, Huafeng
Guo, Zhiming
ADVANCES IN NONLINEAR ANALYSIS, 2023, 12 (01)
[9] NONTRIVIAL PERIODIC SOLUTIONS FOR SECOND-ORDER DIFFERENTIAL DELAY EQUATIONS
Wang, Qi
Liu, Wenjie
Wang, Mei
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2017, 7 (03): : 931 - 941
[10] Multiple periodic solutions for second order impulsive delay differential equations
Dib, Fatima
Daoudi-Merzagui, Naima
INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 2019, 9 (03) : 298 - 312

← 1 2 3 4 5 →