Impulsive integro-differential equations and stability of moving invariant manifolds (Q937368)

Under certain technical assumptions, an invariant and uniformly asymptotically stable manifold is found for the system of impulsive integro-differential equations \[ \begin{cases}\dot{x}(t)=F(t,x(t),\int_{t_0}^t g(t,s,x(s)\,ds,\lambda),& t\neq\tau_k,\\ x(\tau_k+0)-x(\tau_k-0)=I_k(x(\tau_k),\lambda),& k=1,3,3,\ldots,\\ x(t_0+0)=x_0,& t_0\in\mathbb{R}^{+},\end{cases} \] where \(t_0=\tau_0<\tau_1<\ldots<\tau_k<\ldots\), \(\tau_k\to+\infty\).