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On linear impulse systems for functional-differential equations. (English. Russian original) Zbl 0615.34064
Sov. Math., Dokl. 33, 220-223 (1986); translation from Dokl. Akad. Nauk SSSR 286, 1037-1040 (1986).
The problem dealt with is \[ (1)\quad \dot x(t)+A(t)x(t)=f(t),\quad t\neq t_ i,\quad (2)\quad \Delta x(t_ i)=x(t_ i+0)-x(t_ i-0)=b_ ix(t_ i-0)+\beta_ i, \] when (1) is replaced by a functional- differential equation, and the conditions (2) are replaced by \((3)\quad \Delta x(t_ i)=\eta_ j(x)+\beta_ i,\eta_ i\) being linear functionals. This can be regarded as a generalization of the theory of linear impulse systems.
Reviewer: V.C.Boffi

MSC:
34K10 Boundary value problems for functional-differential equations
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