arXiv subjects
Publications and source records attributed to Ioan-Lucian Popa.
In this paper we consider some concepts of exponential splitting for nonautonomous linear discrete-time systems. These concepts are generalizations of some well-known concepts of (uniform and nonuniform) exponential dichotomies. Connections between these concepts are presented and some illustrating examples prove that these are distinct.
The present paper considers a concept of $(h,k,μ,ν)-$trichotomy for noninvertible linear time-varying systems in Hilbert spaces. This work provides a characterization for linear time-varying systems that admits a $(h,k,μ,ν)-$trichotomy in terms of two coupled systems having a $(h,μ,ν)-$dichotomy.
The aim of this paper is to present necessary and sufficient conditions for nonuniform power instability property of linear discrete-time systems in Banach spaces. A characterization of the nonuniform power instability in terms of Lyapunov sequences is also given.
In this paper we investigate four concepts of exponential stability for difference equations in Banach spaces. Characterizations of these concepts are given. They can be considered as variants for the discrete-time case of the classical results due to E.A. Barbashin [2] and R. Datko [5]. An illustrative example clarifies the relations between these concepts.
In this paper we investigate the power instability properties and give necessary and sufficient conditions for the concepts of uniform power instability, power instability and strong power instability for linear discrete-time system $x_{n+1} = A(n)x_{n}$ in Banach spaces.
In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. We motivate our approach by illustrative examples.