On uniform asymptotic stability for nonlinear integro-differential equations of Volterra type
The specifics of the application of Razumikhin technique to the stability analysis of Volterra type integrodifferential equations are considered. The equation can be nonlinear and nonautonomous. We propose new sufficient conditions for uniform asymptotic stability of the zero solution using the phase space of a special construction and constraints on the right side of the equation. In
the presented constraints we can analyze stability, relying not only on the behavior of the auxiliary function along the solutions, but also on the properties of the so called limiting equations.
CYBERNETICS AND PHYSICS, Vol. 8, No. 3. 2019, 161-166. https://doi.org/10.35470/2226-4116-2019-8-3-161-166