CARABALLO GARRIDO , Tomás

Some results on the asymptotic behaviour of solutions of diff erential equations concerning general decay rate are proved. We prove general criteria on the exponential, polynomial, and more general decay properties of solutions by using suitable Lyapunov's functions. We also present a detailed analysis of the perturbed linear and nonlinear di...

Sufficient conditions for pathwise exponential stability of the zero solution of stochastic PDE with deviating argument dxt = Axt dt + Bx (t) dwt are given. The assumptions on the operators A and B are the same that in the case without delay, but the proof is different. In fact, our method shows an alternative proof for the results in the...

Existence and uniqueness of solutions for a class of nonlinear functional differential equations in Hilbert spaces are established. Sufficient conditions which guarantee the transference of exponential stability from partial differential equations to partial functional differential equations are studied. The stability results derived are also...

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