Geodesic
Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale
Electronic journal of differential equations, Tome 2007 (2007)
Zbl   EuDML
Let

$ x^{\Delta}(t) = -a(t)x^{\sigma}(t) + \left(Q(t,x(t), x(t-g(t))))\right)^{\Delta} + G\big(t,x(t), x(t-g(t))\big), t \in \mathbb{T}, $

has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the contraction mapping principle. Also, by the aid of the contraction mapping principle we study the asymptotic stability of the zero solution provided that $Q(t,0,0)= G(t,0,0) = 0$.
Classification : 34K13, 34C25, 34G20
Keywords: Krasnoselskii, contraction mapping, neutral, nonlinear, delay, time scales, periodic solution, unique solution, stability 
Kaufmann,  Eric R.; Raffoul,  Youssef N. Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a82/
@article{EJDE_2007__2007__a82,
     author = {Kaufmann,  Eric R. and Raffoul,  Youssef N.},
     title = {Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1118.34058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a82/}
}
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