STABILITY FOR A FUNCTIONAL DIFFERENTIAL EQUATION IN HILBERT SPACE

Abstract

The stability for the functional differential equation: du/dt = Au(t)+bu(t)+(a*Au)(t) is studied, where A is the infinitesimal generator of a linear dynamical system in Hilbert space and the convolution term contains a square integrable real function a. Sufficient conditions for the asymptotic stability of the solution u are obtained. The results are applied to a retarded partial integrodifferential equation.