Learn More
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)
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)
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)
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)