Some stability and boundedness criteria for a class of Volterra integro-differential systems

J. Vanualailai, University of the South Pacific, Suva, FIJI

E. J. Qualitative Theory of Diff. Equ., No. 12. (2002), pp. 1-20.

Abstract: Using Lyapunov and Lyapunov-like functionals, we study the stability and boundedness of the solutions of a system of Volterra integrodifferential equations. Our results, also extending some of the more well-known criteria, give new sufficient conditions for stability of the zero solution of the nonperturbed system, and prove that the same conditions for the perturbed system yield boundedness when the perturbation is $L^2$.

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