Electron. J. Diff. Eqns., Vol. 2001(2001), No. 05, pp. 1-17.

On the decay rate of solutions of non-autonomous differential systems

Tomas Caraballo

Some results on the asymptotic behaviour of solutions of differential 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 differential systems. The theory is illustrated with several examples.

Submitted December 7, 2000. Published January 3, 2001.
Math Subject Classifications: 34D05, 34D10, 34D20.
Key Words: Asymptotic behaviour, exponential and polynomial stability, rate of decay.

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Tomas Caraballo
Departamento de Ecuaciones Diferenciales y Analisis Numerico
Universidad de Sevilla
Apdo. de Correos 1160
41080-Sevilla, Spain
e-mail: caraball@us.es

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