Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales
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 neut...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/516476 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832545361043914752 |
|---|---|
| author | Yongkun Li Chao Wang |
| author_facet | Yongkun Li Chao Wang |
| author_sort | Yongkun Li |
| collection | DOAJ |
| description | 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)∈T0(x),Δt|(t,x)∈S2i=Πi1(t,x)-t, Δx|(t,x)∈S2i=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, T0(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. |
| format | Article |
| id | doaj-art-40be5f156943410e93f61b15ba839623 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-40be5f156943410e93f61b15ba8396232025-02-03T07:26:05ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/516476516476Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time ScalesYongkun Li0Chao Wang1Department of Mathematics, Yunnan University, Yunnan, Kunming 650091, ChinaDepartment of Mathematics, Yunnan University, Yunnan, Kunming 650091, ChinaUsing 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)∈T0(x),Δt|(t,x)∈S2i=Πi1(t,x)-t, Δx|(t,x)∈S2i=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, T0(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.http://dx.doi.org/10.1155/2012/516476 |
| spellingShingle | Yongkun Li Chao Wang Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales Journal of Applied Mathematics |
| title | Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales |
| title_full | Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales |
| title_fullStr | Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales |
| title_full_unstemmed | Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales |
| title_short | Three Positive Periodic Solutions to Nonlinear Neutral Functional Differential Equations with Parameters on Variable Time Scales |
| title_sort | three positive periodic solutions to nonlinear neutral functional differential equations with parameters on variable time scales |
| url | http://dx.doi.org/10.1155/2012/516476 |
| work_keys_str_mv | AT yongkunli threepositiveperiodicsolutionstononlinearneutralfunctionaldifferentialequationswithparametersonvariabletimescales AT chaowang threepositiveperiodicsolutionstononlinearneutralfunctionaldifferentialequationswithparametersonvariabletimescales |