Abstract
In furthering the results obtained earlier in [1,2] general stability theorems using sign-constant Liapunov functions are established for neutral nonlinear systems with a deviating argument. Concepts connected with the stability of auxiliary difference inequalities play on essential role. The application of Liapunov's methods to the study of the stability of systems of neutral equations [5] has been examined in a number of papers [1 – 4]. A method for studying the stability of neutral systems by using only sign-constant but not sign-definite Liapunov functionals was proposed in [1]. This method was used in [2] to obtain stability conditions for first-order neutral nonlinear equations. An analogous method was used in [4] to investigate the stability of solutions of neutral equations with a linear neutral part.
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