Asymptotic behavior of impulsive differential equations (Q1915750)

This is one of the first works devoted to the study of asymptotic behaviour of solutions of the following impulsive system: \(x' = f(t,x)\), \(t \neq t_i\), \(\Delta x(t_i) = \varphi_i (x(t_i))\), \(t_i \to + \infty\), \((t,x) \in \mathbb{R}_+ \times \mathbb{R}^n\). Here, the authors give the simple conditions under which this system has an asymptotic equilibrium at \(+ \infty\). It should be noted that this paper was received for publication on August, 1992 and the newest results in this direction can be found in the monograph [\textit{D. D. Bainov} and \textit{P. S. Simeonov}, Impulsive differential equations: asymptotic properties of the solutions, World Scientific (1995; Zbl 0828.34002)].