STABILITY BY DECOMPOSITIONS FOR VOLTERRA EQUATIONS

Abstract

We consider a system of integrodifferential equations of the form
(1) x' = A(t)x + ∫_0^t {C(t, s)x(s)ds}
which we then write as
(2) x' = L(t)x + ∫_0^t {{C_1}} (t, s)x(s)ds + ({d \over {dt}})∫_0^t {H(t, s)x(s)ds} .
A number of Lyapunov functionals are constructed for (2) yielding necessary and sufficient conditions for stability of the zero solution of (1).