Dishliev, A. B.; Bainov, D. D. Continuous dependence of the solution of a system of differential equations with impulses on the impulse hypersurfaces. (English) Zbl 0674.34005 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 Cited in 1 ReviewCited in 7 Documents 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 PDF BibTeX XML Cite \textit{A. B. Dishliev} and \textit{D. D. Bainov}, J. Math. Anal. Appl. 135, No. 2, 369--382 (1988; Zbl 0674.34005) Full Text: DOI References: [1] Mil’man, V.D; Myshkis, A.D, On stability of motion in the presence of impulses, Sibirian math. J., 1, No. 2, 233-237, (1960), [Russian] · Zbl 1358.34022 [2] Mil’man, V.D; Myshkis, A.D, Random impulses in linear dynamical systems, (), 64-81, [Russian] · Zbl 0133.10403 [3] Samoilenko, A.M; Perestjuk, N.A, Stability of the solutions of differential equations with impulse effect, Differensial’nye uravneniya, 11, 1981-1992, (1977), [Russian] [4] Raghavendra, V; Rao, R.M, On stability of differential systems with respect to impulsive perturbations, J. math. anal. appl., 48, 515-526, (1974) · Zbl 0303.34042 [5] Halanai, A; Veksler, D, Qualitative theory of impulse systems, (1974), Mir Moscow, [Russian] [6] Pandit, S.G; Deo, S.G, Differential systems involving impulses, (1982), Springer-Verlag New York/Berlin · Zbl 0417.34085 [7] Dishliev, A.B; Bainov, D.D, Sufficient conditions for absence of “beating” in systems of differential equations with impulses, Appl. anal., 18, 67-73, (1984) · Zbl 0596.34016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.