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Advanced impulsive differential equations with piecewise constant arguments. (English) Zbl 1218.34095

Differential equations with piecewise constant arguments are related to difference and differential equations. In this paper, the authors are interested in such equations with impulses. They start by proving the existence and uniqueness of solutions. Then they give necessary and sufficient conditions for the existence of periodic solutions. The paper is completed by a result on oscillations and nonoscillations and a result on the asymptotical stability of the null solution.

MSC:

34K45 Functional-differential equations with impulses
34K11 Oscillation theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K13 Periodic solutions to functional-differential equations
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