Stability results for neutral integro-differential equations with multiple functional delays

Abstract

Necessary and sufficient conditions for the zero solution of the nonlinear neutral integro-diferential equation d dt r(t) hx(t) + Q(t, x(t − g1(t)), ..., x(t − gN (t)))i = −a(t)x(t) +Xi=1 Z t t−gi(t) ki(t, s)fi(x(s))ds to be asymptotically stable are obtained. In the process we invert the integro differential equation and obtain an equivalent integral equation. The contraction mapping principle is used as the main mathematical tool for establishing the necessary and sufficient conditions