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- Adina Luminita Sasu
- Appl. Math. Lett.
- 2006

We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair (Lp(R,X),Lq(R,X)). We show that the admissibility of the pair (Lp(R,X),Lq(R,X)) is equivalent to the uniform exponential dichotomy of an evolution family if and only if p ≥ q. As applications we obtain… (More)

- A. L. Sasu
- 2005

We associate a discrete-time equation to an exponentially bounded semigroup and we characterize the exponential instability of the semigroup in terms of the complete admissibility of the pair (l ∞ (N, X), l ∞ (N, X)). As a consequence, we obtain that in certain conditions a C 0-semigroup is exponentially unstable if and only if the pair (C b (R + , X), C b… (More)

This paper is concerned with systems with control whose state evolution is described by linear skew-product semiflows. The connection between uniform exponential stability of a linear skew-product semiflow and the stabilizability of the associated system is presented. The relationship between the concepts of exact con-trollability and complete… (More)

In this paper, we use the Leray–Schauder degree theory to establish new results on the existence and uniqueness of anti-periodic solutions for a class of nonlinear nth-order differential equations with two deviating arguments of the form x (n) (t) + f (t, x (n−1) (t)) + g 1 (t, x(t − τ 1 (t))) + g 2 (t, x(t − τ 2 (t))) = e(t). As an application, we also… (More)

and Applied Analysis 3 We consider the general setting of variational equations described by skew-product flows, and we associate a control system on the real line. Beside obtaining new conditions for the existence of uniform or exponential dichotomy of skew-product flows, the main aim is to clarify the chart of the connections between the classes of… (More)

In this paper we give necessary and sufficient conditions for uniform exponential instability of evolution families in Banach spaces, in terms of Banach function spaces. Versions of some well-known theorems due to Datko, Neerven, Rolewicz and Zabczyk, are obtained for the case of uniform exponential instability of evolution families.

- Alaa E. Hamza, Moneer A. Al-Qubaty, Adina Luminiţa Sasu
- 2012

In this paper, we investigate some properties of the operator exponential solutions of the initial value problem X ∆ (t) = A(t)X(t), t ∈ T X(s) = I, where I is the identity operator on a Banach space X, s is an initial point in a time scale T and A(t) is a bounded linear operator on X, t ∈ T. Also, we give an example of differentiable 2 × 2 matrices A(t)… (More)

- Adina Luminita Sasu, Bogdan Sasu
- Asymptotic Analysis
- 2010