A new approach to impulsive retarded differential equations: stability results

Marcia Federson, Stefan Schwabik


It is known that impulsive retarded functional differential equations can be regarded as Banach-space valued generalized ordinary differential equations (generalized ODEs). In the present paper, we discuss the variational stability and variational asymptotic stability of the zero solution of generalized ODEs and we apply these results to obtain the Lyapunov uniform stability and uniform asymptotic stability for a large class of retarded differential equations with pre-assigned moments of impulse action, via Lyapunov functionals.

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