Continuous dependence of the solution of a system of differential equations with impulses on the impulse hypersurfaces. (English) Zbl 0674.34005

Dishliev, A. B.; Bainov, D. D.

J. Math. Anal. Appl. 135, No. 2, 369-382 (1988).

The authors consider the Cauchy problem for the differential system \(x'=f(t,x)\), \(t\neq t_ i\) \((i=1,2,...)\), \(x\in D\subset R^ n\) with the impulses \(x(t_ i+)-x(t_ i)=I_{j_ i}(x(t_ i))\) where \(x(t_ i)\) belongs to a surface \(S_ i\). Some results on the continuous dependence of solution on the impulse surfaces \(S_ i\) are given.

Reviewer: N.H.Pavel

MSC:

34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Keywords:

Cauchy problem; impulses

References:

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