کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
758399 | 896426 | 2012 | 9 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Existence of periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale Existence of periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale](/preview/png/758399.png)
Let TT be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to Burton to prove the existence of periodic solutions on time scale of the nonlinear dynamic equation with variable delay.x▵(t)=-a(t)x3(σ(t))+c(t)x▵∼(t-r(t))+G(t,x3(t),x3(t-r(t))),t∈T,where f▵ is the ▵-derivative on TT and f▵∼ is the ▵-derivative on (id-r)(T)(id-r)(T). We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the Burton–Krasnoselskii’s theorem. The results obtained here extend the works of Deham and Djoudi [8] and [9] and Ardjouni and Djoudi [2].
► In this work we use an interesting hybrid fixed point theorem due to Krasnoseskii–Burton.
► We prove the existence of periodic solutions for neutral nonlinear dynamic equation with variable delays.
► This study is made on a time scale which unifies theories of differential equations and difference equations.
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 17, Issue 7, July 2012, Pages 3061–3069