Boundedness and asymptotic stability of nonlinear Volterra integro-differential equations using Lyapunov functional.

In this paper, I consider Lyapunov functionals combined with the Laplace transform to obtain boundedness results regarding the solutions of the nonlinear Volterra integro-differential equations x ′ (t) = A (t) x (t) + B (t) + ∫ 0 t C (t , s) f (x (s)) ds + g (x (t)). Asymptotic stability results regarding the zero solution are carried out for the case where B (t) is identically zero. Numerical examples are proposed to perform the given results. [ABSTRACT FROM AUTHOR]