Nonautonomous Systems with Variable Moments of Impulses

Marat Akhmet ()
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Marat Akhmet: Middle East Technical University, Department of Mathematics

Chapter Chapter 5 in Principles of Discontinuous Dynamical Systems, 2010, pp 55-80 from Springer

Abstract: Abstract Let $$G \subset {\mathbb{R}}^{n}$$ be an open and connected set, I an open interval in $$\mathbb{R},$$ and $$\mathcal{A}$$ an interval in $$\mathbb{Z}.$$ We consider the following system: 5.1 $$\begin{array}{rcl} & & x^\prime = f(t,x), \\ & & \Delta x{\vert }_{t={\tau }_{i}(x)} ={J}_{i}(x),\end{array}$$ where $$(t,i,x) \in I \times \mathcal{A}\times G,$$ the function f(t, x) is continuous on I ×G, functions J i are defined on G, and $${\tau }_{i}(x),i \in \mathcal{A},$$ are continuous on G functions.

Keywords: Continuous Dependence; Maximal Interval; Impulsive Differential Equation; Impulsive System; Piecewise Continuous Function (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-6581-3_5

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DOI: 10.1007/978-1-4419-6581-3_5

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