Existence of periodic solutions for a class of second-order superquadratic delay differential equations

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

Existence of periodic solutions for a class of second-order superquadratic delay differential equations

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

Mathematics

Guangdong University of Technology
King Abdulaziz University
Sun Yat-Sen University
Texas A&M University-Kingsville

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

8 Citations (Scopus)

Abstract

Using critical point theory (in particular a Linking theorem) we study the existence of periodic solutions for the second-order delay differential equations x '' (t) = -f(t; x(t - τ)); where f(t; x) depends periodically on t and F(t; x) is superquadratic (here ?xF = f). In particular we consider the case when f does not satisfy the Ambrosetti-Rabinowitz growth condition.

Original language	English
Pages (from-to)	405-419
Number of pages	15
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume	21
Issue number	5
Publication status	Published - 2014

Keywords

Critical point theory
Delay differential equations
Linking theorem
Superquad-ratic growth condition

Cite this

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title = "Existence of periodic solutions for a class of second-order superquadratic delay differential equations",

abstract = "Using critical point theory (in particular a Linking theorem) we study the existence of periodic solutions for the second-order delay differential equations x '' (t) = -f(t; x(t - τ)); where f(t; x) depends periodically on t and F(t; x) is superquadratic (here ?xF = f). In particular we consider the case when f does not satisfy the Ambrosetti-Rabinowitz growth condition.",

keywords = "Critical point theory, Delay differential equations, Linking theorem, Superquad-ratic growth condition",

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

note = "Publisher Copyright: Copyright {\textcopyright} 2014 Watam Press.",

year = "2014",

language = "English",

volume = "21",

pages = "405--419",

journal = "Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis",

issn = "1201-3390",

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Existence of periodic solutions for a class of second-order superquadratic delay differential equations. / Guo, Chengjun; O'Regan, Donal; Xu, Yuantong et al.
In: Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, Vol. 21, No. 5, 2014, p. 405-419.

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

TY - JOUR

T1 - Existence of periodic solutions for a class of second-order superquadratic delay differential equations

AU - Guo, Chengjun

AU - O'Regan, Donal

AU - Xu, Yuantong

AU - Agarwal, Ravi P.

PY - 2014

Y1 - 2014

N2 - Using critical point theory (in particular a Linking theorem) we study the existence of periodic solutions for the second-order delay differential equations x '' (t) = -f(t; x(t - τ)); where f(t; x) depends periodically on t and F(t; x) is superquadratic (here ?xF = f). In particular we consider the case when f does not satisfy the Ambrosetti-Rabinowitz growth condition.

AB - Using critical point theory (in particular a Linking theorem) we study the existence of periodic solutions for the second-order delay differential equations x '' (t) = -f(t; x(t - τ)); where f(t; x) depends periodically on t and F(t; x) is superquadratic (here ?xF = f). In particular we consider the case when f does not satisfy the Ambrosetti-Rabinowitz growth condition.

KW - Critical point theory

KW - Delay differential equations

KW - Linking theorem

KW - Superquad-ratic growth condition

UR - https://www.scopus.com/pages/publications/84908598881

M3 - Article

AN - SCOPUS:84908598881

SN - 1201-3390

VL - 21

SP - 405

EP - 419

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

IS - 5

ER -

Existence of periodic solutions for a class of second-order superquadratic delay differential equations

Abstract

Keywords

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