Datko criteria for uniform instability in Banach spaces (original) (raw)

On Uniform Instability with Growth Rates in Banach Spaces

Carpathian Journal of Mathematics

The paper considers three concepts of uniform instability for evolution operators: uniform exponential instability, uniform polynomial instability and uniform h-instability. Some characterizations of these notions and connections between these concepts are given.

On Nonuniform Exponential Instability of Operators in Banach Spaces

Analele Universitatii de Vest din …, 2011

The paper considers two concepts of nonuniform exponential instability in infinite-dimensional spaces. Our main objectives are to give characterizations for these concepts and to establish relations between them. The obtained results are generalizations of some well-known stability theorems due to L

Integral Characterizations for Uniform Stability with Growth Rates in Banach Spaces

Axioms

The aim of this paper is to present some integral characterizations for the concept of uniform stability with growth rates in Banach spaces. In this sense, we prove necessary and sufficient conditions (of Barbashin and Datko type) for an evolution operator to be uniform h- stable. As particular cases of this notion, we obtain four characterizations for uniform exponential stability and two characterizations for uniform polynomial stability.

On Barreira-Valls polynomial stability of evolution operators in Banach spaces

Electronic Journal of Qualitative …, 2011

Our main objective is to consider a concept of nonuniform behavior and obtain appropriate versions of the well-known stability due to R. Datko and L. Barbashin. This concept has been considered in the works of L. Barreira and C. Valls. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability.

On (h, k)-stability of evolution operators in Banach spaces

Applied Mathematics Letters, 2011

The main aim of this work is to define and exemplify various stability concepts and to emphasize connections between them. These stability concepts are included in a general concept, the so-called (h, k)-stability. We motivate our approach with illustrative examples.

On Some Characterizations for Uniform Dichotomy of Evolution Operators in Banach Spaces

Mathematics

The present paper deals with two of the most significant behaviors in the theory of dynamical systems: the uniform exponential dichotomy and the uniform polynomial dichotomy for evolution operators in Banach spaces. Assuming that the evolution operator has uniform exponential growth, respectively uniform polynomial growth, we give some characterizations for the uniform exponential dichotomy, respectively for the uniform polynomial dichotomy. The proof techniques that we use for the polynomial case are new. In addition, connections between the concepts approached are established.

Barbashin conditions for uniform instability of evolution operators

Studia Universitatis Babes-Bolyai Matematica, 2021

The aim of the present paper is to give some characterization theorems of Barbashin type for the uniform exponential instability and uniform polynomial instability behavior of evolution operators. Also, some examples which illustrate the connections between the concepts presented are given.

On a logarithmic criterion for uniform polynomial stability

Annals of West University of Timisoara - Mathematics and Computer Science, 2018

The paper presents a logarithmic criterion for uniform polynomial stability of evolution operators in Banach spaces. As applications, another four characterizations of uniform polynomial stability are obtained.

Robust Stability of Linear Evolution Operators on Banach Spaces

SIAM Journal on Control and Optimization, 1994

In this paper we introduce a stability radius for a wide class of linear infinite-dimensional time-varying systems under structured time-varying perturbations. A framework is presented which allows the same degree of unboundedness in the perturbations as in the generator of the nominal model.