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

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.

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)

In this paper we consider a nonuniform unstability concept for evolution operators in Banach spaces. The relationship between this concept and the Perron condition is studied. Generalizations to the nonuniform case of some results of Van Minh, Räbiger and Schnaubelt are obtained. The theory we present here is applicable for general time varying linear… (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)

- 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 C0-semigroup is exponentially unstable if and only if the pair (Cb(R+, X),Cb(R+, X)) is… (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 skewproduct semiflow and the stabilizability of the associated system is presented. The relationship between the concepts of exact controllability and complete stabilizability… (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(t) + f(t, x(n−1)(t)) + g1(t, x(t− τ1(t))) + g2(t, x(t− τ2(t))) = e(t). As an application, we also give an example to… (More)

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

- Hugo Leiva, Nelson Merentes, Jose Luis Sanchez, Ambrosio Tineo Moya, Adina Luminiţa Sasu
- 2015

In this paper we give a necessary and sufficient conditions for approximate controllability of a wide class of semilinear nonautonomous systems in Hilbert spaces. This is done by employing skew-product semi-flows technique. As an application we prove the approximate controllability of a broad class of nonautonomous semilinear reaction diffusion equations… (More)