Use of forms of high order in discussions of the stability of systems of differential equations with delay

A method of investigating forms of arbitrarily high order with respect to sign-definiteness in some cone of the space Rⁿ that coincides with a coordinate angle is given. The results obtained allowed us to use such functions as Lyapunov functions for the study of questions of stability for systems of differential equations with delayed argument.Translated from Dinamicheskie Sistemy, No. 9, pp. 15–21, 1990.