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Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-28, 28 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-03-07
Country of Publication
Egypt
No. of Pages
28
Main Subjects
Abstract EN
Using two successive reductions: B-equivalence of the system on a variable time scale to a system on a time scale and a reduction to an impulsive differential equation and by Leggett-Williams fixed point theorem, we investigate the existence of three positive periodic solutions to the nonlinear neutral functional differential equation on variable time scales with a transition condition between two consecutive parts of the scale (d/dt)(x(t)+c(t)x(t-α))=a(t)g(x(t))x(t)-∑j=1nλjfj(t,x(t-vj(t))), (t,x)∈?0(x),Δt|(t,x)∈?2i=Πi1(t,x)-t, Δx|(t,x)∈?2i=Πi2(t,x)-x, where Πi1(t,x)=t2i+1+τ2i+1(Πi2(t,x)) and Πi2(t,x)=Bix+Ji(x)+x, i=1,2,….
λj (j=1,2,…,n) are parameters, ?0(x) is a variable time scale with (ω,p)-property, c(t), a(t), vj(t), and fj(t,x) (j=1,2,…,n) are ω-periodic functions of t, Bi+p=Bi, Ji+p(x)=Ji(x) uniformly with respect to i∈ℤ.
American Psychological Association (APA)
Li, Yongkun& Wang, Chao. 2012. Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-993331
Modern Language Association (MLA)
Li, Yongkun& Wang, Chao. Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales. Journal of Applied Mathematics No. 2012 (2012), pp.1-28.
https://search.emarefa.net/detail/BIM-993331
American Medical Association (AMA)
Li, Yongkun& Wang, Chao. Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-28.
https://search.emarefa.net/detail/BIM-993331
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993331