About asymptotic stability of solutions of the linear Volterra integro - differential equation of the third order with incomplete kernels

Sufficient conditions of asymptotic stability of solutions of linear integro-differential equation of Volterra type with incomplete kernels on the semi axles are established. For this, the method of auxiliary kernels, the non-standard method of reduction to the system, the method of squaring equations, V. Volterra method of transformation of the equations, method of cutting functions, YU.A. Ved’s, Z. Pakhirov’s method of integral inequalities, Lusternik-Sobolev lemma. An illustrative example is constructed showing the naturalness of the imposed conditions.