This paper is concerned with the nonlinear system x t ft, xt. We give a converse Lyapunov theorem and prove robustness of uniform exponential dissipativity with respect to unbounded external perturbations, without assuming f being globally Lipschitz in x.

In this paper we present Lyapunov based proofs for the well-known Arendt-Batty-Lyubich-Vũ Theorem for strongly continuous and discrete semigroups. We also study the spectral properties of the limit isometric groups used in the proofs.

The stability of stochastic delayed Cellular Neural Networks (DCNN) is investigated in this paper. Using suitable Lyapunov functional and the semimartingale convergence theorem, we obtain some sufficient conditions for checking the almost sure exponential stability of the DCNN.

This paper studies the homotopy invariant cat(X, ξ) introduced in [5]. Given a finite cell-complex X, we study the function ξ → cat(X, ξ) where ξ varies in the cohomology space H 1 (X; R). Note that cat(X, ξ) turns into the classical Lusternik-Schnirelmann category cat(X) in the case ξ = 0. Interest in cat(X, ξ) is based on its applications in dynamics where it enters estimates of complexity of...

We study linear fractional boundary value problems consisting of an α-th order Riemann-Liouville fractional differential equation with 2 < α ≤ 3 and certain fractional boundary conditions. We derive several Lyapunovtype inequalities and apply them to establish nonexistence, uniqueness, and existence-uniqueness of solutions for related homogeneous and nonhomogeneous linear fractional boundary va...