Geodesic
Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
@article{EJDE_2007__2007__a282,
     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},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a282/}
}
TY  - JOUR
AU  - Kaufmann, Eric R.
AU  - Raffoul, Youssef N.
TI  - Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale
JO  - Electronic Journal of Differential Equations
PY  - 2007
VL  - 2007
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a282/
LA  - en
ID  - EJDE_2007__2007__a282
ER  - 
%0 Journal Article
%A Kaufmann, Eric R.
%A Raffoul, Youssef N.
%T Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale
%J Electronic Journal of Differential Equations
%D 2007
%V 2007
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a282/
%G en
%F EJDE_2007__2007__a282
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__a282/