Inequalities and exponential stability and instability in finite delay Volterra integro-differential equations

Abstract

We use Liapunov functionals to obtain sufficient conditions that ensure exponential stability of the nonlinear Volterra integro- differential equation x(2) (t) = p(1)x(t) - integral(t)(t-iota) q(t,s)x(s)ds where the constant t is positive, the function p does not need to obey any sign condition and the kernel q is continuous. Our results improve the results obtained in literature even in the autonomous case. In addition, we give a new criteria for instability.