Periodic solutions for neutral functional differential equations with impulses on time scales
Let $mathbb{T}$ be a periodic time scale. We use Krasnoselskii's fixed point theorem to show that the neutral functional differential equation with impulses $$displaylines{ x^{Delta}(t)=-A(t)x^sigma(t)+g^Delta(t,x(t-h(t)))+f(t,x(t),x(t-h(t))),quad teq t_j,;tinmathbb{T},cr x(t_j^+)= x(t_j^...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2012-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/57/abstr.html |
| Summary: | Let $mathbb{T}$ be a periodic time scale. We use Krasnoselskii's fixed point theorem to show that the neutral functional differential equation with impulses $$displaylines{ x^{Delta}(t)=-A(t)x^sigma(t)+g^Delta(t,x(t-h(t)))+f(t,x(t),x(t-h(t))),quad teq t_j,;tinmathbb{T},cr x(t_j^+)= x(t_j^-)+I_j(x(t_j)), quad jin mathbb{Z}^+ }$$ has a periodic solution. Under a slightly more stringent conditions we show that the periodic solution is unique using the contraction mapping principle. |
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| ISSN: | 1072-6691 |