Paper Title:

Polynomial Dichotomy of C₀-Quasi Semigroups in Banach Spaces

Author(s):

Sutrima^1,2, Christiana Rini Indrati², Lina Aryati²

¹Department of Mathematics,
Universitas Sebelas Maret,
PO Box 57126, Surakarta,
Indonesia.
E-mail: sutrima@mipa.uns.ac.id

²Department of Mathematics,
Universitas Gadjah Mada,
PO Box 55281, Yogyakarta,
Indonesia.
E-mail: rinii@ugm.ac.id, lina@ugm.ac.id 

Abstract:

Stability of solutions of the problems is an important aspect for application purposes. Since its introduction by Datko [7], the concept of exponential stability has been developed in various types of stability by various approaches. The existing conditions use evolution operator, evolution semigroup, and quasi semigroup approach for the non-autonomous problems and a semigroup approach for the autonomous cases. However, the polynomial stability based on C₀-quasi semigroups has not been discussed in the references. In this paper we propose a new stability for C₀-quasi semigroups on Banach spaces i.e the polynomial stability and polynomial dichotomy. As the results, the sufficient and necessary conditions for the polynomial and uniform polynomial stability are established as well as the sufficiency for the polynomial dichotomy. The results are also confirmed by the examples.

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