Existence of homoclinic orbits of a class of second-order differential difference equations

Chengjun Guo; Donal O'Regan; Yuantong Xu; Ravi P. Agarwal

Existence of homoclinic orbits of a class of second-order differential difference equations

Chengjun Guo
, Donal O'Regan
, Yuantong Xu
, Ravi P. Agarwal

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

20 Citations (Scopus)

Abstract

This paper is concerned with the existence of homoclinic orbits of the second order differential difference equations containing both advance and retardation z̈(t) - K_z(t, z(t)) + f(t, z(t + τ), z(t); z(t - τ)) = h(t). Using critical point theory we show a nontrivial homoclinic orbit is obtained as a limit of a sequence of periodic solutions of the equation.

Original language	English
Pages (from-to)	653-668
Number of pages	16
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Volume	20
Issue number	6
Publication status	Published - 2013

Keywords

Critical point theory
Differential difference equation
Homoclinic solutions

Cite this

@article{28e456a9e4154a29a7641c3f038984c1,

title = "Existence of homoclinic orbits of a class of second-order differential difference equations",

abstract = "This paper is concerned with the existence of homoclinic orbits of the second order differential difference equations containing both advance and retardation {\"z}(t) - Kz(t, z(t)) + f(t, z(t + τ), z(t); z(t - τ)) = h(t). Using critical point theory we show a nontrivial homoclinic orbit is obtained as a limit of a sequence of periodic solutions of the equation.",

keywords = "Critical point theory, Differential difference equation, Homoclinic solutions",

author = "Chengjun Guo and Donal O'Regan and Yuantong Xu and Agarwal, \{Ravi P.\}",

year = "2013",

language = "English",

volume = "20",

pages = "653--668",

journal = "Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms",

issn = "1492-8760",

publisher = "Watam Press",

number = "6",

}

TY - JOUR

T1 - Existence of homoclinic orbits of a class of second-order differential difference equations

AU - Guo, Chengjun

AU - O'Regan, Donal

AU - Xu, Yuantong

AU - Agarwal, Ravi P.

PY - 2013

Y1 - 2013

N2 - This paper is concerned with the existence of homoclinic orbits of the second order differential difference equations containing both advance and retardation z̈(t) - Kz(t, z(t)) + f(t, z(t + τ), z(t); z(t - τ)) = h(t). Using critical point theory we show a nontrivial homoclinic orbit is obtained as a limit of a sequence of periodic solutions of the equation.

AB - This paper is concerned with the existence of homoclinic orbits of the second order differential difference equations containing both advance and retardation z̈(t) - Kz(t, z(t)) + f(t, z(t + τ), z(t); z(t - τ)) = h(t). Using critical point theory we show a nontrivial homoclinic orbit is obtained as a limit of a sequence of periodic solutions of the equation.

KW - Critical point theory

KW - Differential difference equation

KW - Homoclinic solutions

UR - https://www.scopus.com/pages/publications/84891351497

M3 - Article

SN - 1492-8760

VL - 20

SP - 653

EP - 668

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

IS - 6

ER -

Existence of homoclinic orbits of a class of second-order differential difference equations

Abstract

Keywords

Other files and links

Fingerprint

Cite this