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