Geodesic
Impulsive dynamic equations on a time scale
Electronic journal of differential equations, Tome 2008 (2008)
Let

$\displaylines{ y^{\Delta}(t) = -a(t)y^{\sigma}(t)+ f ( t, y(t) ),\quad t \in (0, T],\cr y(0) = 0,\cr y(t_i^+) = y(t_i^-) + I (t_i, y(t_i) ), \quad i = 1, 2, \dots, n, }$

where $y(t_i^\pm) = \lim_{t \to t_i^\pm} y(t)$, and $y^\Delta$ is the $\Delta$-derivative on $\mathbb{T}$, has a solution. Under a slightly more stringent inequality we show that the solution is unique using the contraction mapping principle. Finally, with the aid of the contraction mapping principle we study the stability of the zero solution on an unbounded time scale.
Classification : 34A37, 34A12, 39A05
Keywords: fixed point theory, nonlinear dynamic equation, stability, impulses 
@article{EJDE_2008__2008__a20,
     author = {Kaufmann,  Eric R. and Kosmatov,  Nickolai and Raffoul,  Youssef N.},
     title = {Impulsive dynamic equations on a time scale},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1184.34091},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a20/}
}
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AU  - Raffoul,  Youssef N.
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VL  - 2008
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%A Raffoul,  Youssef N.
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%F EJDE_2008__2008__a20
Kaufmann,  Eric R.; Kosmatov,  Nickolai; Raffoul,  Youssef N. Impulsive dynamic equations on a time scale. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a20/