The Lyusternik‒Sobolev lemma and the specific asymptotic stability of solutions of linear homogeneous Volterra-type integro-differential equations of order 3

Abstract

Sufficient conditions for the asymptotic stability on a half-line of the solutions of a linear homogeneous Volterra-type integro-differential equation of order 3 in the case where the solutions of the corresponding linear homogeneous differential equation are asymptotically unstable are determined. A new method is proposed, and an illustrative example is constructed.