Convergence to a constant of the solutions of differential equations with impulse effect (Q1118742)

With the help of partially continuous analogues of Lyapunov's functions, necessary and sufficient conditions are found for which the solutions of the systems with impulse effect of the kind \(dx/dt=f(t,x)\), \(t\neq \tau_ k\), \(\Delta x|_{t=\tau_ k}=I_ k(x)\), \(k=1,2,..\). tend exponentially to a constant as \(t\to \infty\).