Polynomial stability of evolution operators in Banach spaces
The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.
On Nonuniform Polynomial Stability for Evolution Operators on the Half-line
The main aim of this paper is to study a concept of nonuniform polynomial stability for evolution operators onthe half-line. The obtained results are variants for nonuniform polynomial stability of some well-known theorems dueto Barbashin, Datko, Rolewicz and Zabczyk in the case of uniform exponential stability. This paper generalizes wellknownresults for the nonuniform exponential stability (Lupa & Megan, 2012) and the uniform polynomial stability(Megan & Ceausu, 2012).
Exponential Instability of Skew-evolution Semiflows in Banach Spaces
This paper introduces a concept of exponential instability for skew-evolution semiflows in Banach spaces. This is defined by means of evolution semiflows and evolution cocycles. The approach is from nonuniform point of view.