Uniform asymptotic stability via Liapunov-Razumikhin technique

Abstract:

The Liapunov-Razumikhin technique is applied to obtain the uniform asymptotic stability for linear integrodifferential equations in Hilbert spaces, \[ x’(t) = A\left [ {x(t) + \int _\# ^t {F(t - s)x(s) ds} } \right ],\quad t \geq {t_0} \geq 0(\# = 0\;{\text {or}} - \infty ),\] which occur in viscoelasticity and in heat conduction for materials with memory.