Solutions instability of Volterra type integro-differential equations

V.S.Sergeev

Dorodnitsyn Computing Center of the Russian Academy of Sciences, Moscow, Russia

Some results on instability in the critical case of zero root are indicated before in our investigation for the Volterra type integro-differential equations under different conditions on integral kernels and nonlinear terms. The algorithm of calculation of the Lyapunov constant has been offered for a case of holomorphic nonlinear terms with continuous coefficients that exponentially tent to constants.

In this article the sufficient conditions of instability are given for a case when power series coefficients are piecewise continuous bounded functions.