Periodic solutions for nonlinear differential equation with functional delay. (English) Zbl 1171.47061

Deham, Hafsia; Djoudi, Ahcene

Georgian Math. J. 15, No. 4, 635-642 (2008).

Applying the fixed point theorem on the sum of two operators due to T.A.Burton [Proc.Am.Math.Soc.124, 2383–2390 (1996; Zbl 0873.45003)], the authors prove the existence of a periodic solution for the following equation with delay \[ x'(t)=-a(t)x^3(t)+G(t,x^3(t-r(t))). \]

Reviewer: Mirosława Zima (Rzeszow)

MSC:

47N20	Applications of operator theory to differential and integral equations
45D05	Volterra integral equations
47H10	Fixed-point theorems
34K13	Periodic solutions to functional-differential equations

Keywords:

Krasnosel’skij’s fixed point theorem; delay; nonlinear integral equation; periodic solution

Citations:

Zbl 0873.45003