Lazer-Leach Type Conditions on Periodic Solutions of Liénard Equation with a Deviating Argument at Resonance
Author
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-05-08
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We study the existence of periodic solutions of Liénard equation with a deviating argument x′′+f(x)x'+n2x+g(x(t-τ))=p(t), where f,g,p:R→R are continuous and p is 2π-periodic, 0≤τ<2π is a constant, and n is a positive integer.
Assume that the limits limx→±∞g(x)=g(±∞) and limx→±∞F(x)=F(±∞) exist and are finite, where F(x)=∫0xf(u)du.
We prove that the given equation has at least one 2π-periodic solution provided that one of the following conditions holds: 2cos(nτ)[g(+∞)-g(-∞)]≠∫02πp(t)sin(θ+nt)dt, for all θ∈[0,2π],2ncos(nτ)[F(+∞)-F(-∞)]≠∫02πp(t)sin(θ+nt)dt, for all θ∈[0,2π],2[g(+∞)-g(-∞)]-2nsin(nτ)[F(+∞)-F(-∞)]≠∫02πp(t)sin(θ+nt)dt, for all θ∈[0,2π],2n[F(+∞)-F(-∞)]-2sin(nτ)[g(+∞)-g(-∞)]≠∫02πp(t)sin(θ+nt)dt, for all θ∈[0,2π].
American Psychological Association (APA)
Wang, Zaihong. 2013. Lazer-Leach Type Conditions on Periodic Solutions of Liénard Equation with a Deviating Argument at Resonance. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-507075
Modern Language Association (MLA)
Wang, Zaihong. Lazer-Leach Type Conditions on Periodic Solutions of Liénard Equation with a Deviating Argument at Resonance. Abstract and Applied Analysis No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-507075
American Medical Association (AMA)
Wang, Zaihong. Lazer-Leach Type Conditions on Periodic Solutions of Liénard Equation with a Deviating Argument at Resonance. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-507075
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-507075