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2013-11-19 Nonlinear Seminar

dr Aneta Sikorska-Nowak
Asymptotic stability of the integro-differential equation with delay

Certainly, the Lyapunov direct method has been, for more than 100 years, the main tool for the study of stability properties of ordinary, functional, integro-differential and partial differential equations. Nevertheless, the applications of this method to problem of stability in differential equations with delay has encountered serious difficulties if the delay is unbounded or if the equation has unbounded terms. The fixed point theory does not only solve the problem on stability but has a significant advantage over Lyapunov’s direct method.

I will present the results on the asymptotic stability of solutions of nonlinear integro-differential equations with delay using Sadovskii Fixed Point Theorem and properties of the measure of noncompactness.