On stability of a second order integro-differential equation

There exists a well-developed stability theory for integro-differential equations of the first order and only a few results on integro-differential equations of the second order. The aim of this paper is to fill up this gap. Explicit tests for uniform exponential stability of linear scalar delay integro-differential equations of the second order x¨(t) + ^Z _{g (} ^t _{t )} G(t, s)x (s)ds + ^Z _h ^t ₍t) H(t, s)x(s)ds = 0 are obtained.