For a class of vector renewal equations arising in the theory of spatially nonuniform chemical reaction processes, stability conditions are given in terms of the physicochemical operators D and K. In particular, we provide conditions for the stability of an initially uniform, multicomponent film bounding a planar catalytic surface, and for the asymptotic stability of a reaction system composed ...

In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...

In this short note we prove a hierarchical stability result that applies to hybrid dynamical systems satisfying the hybrid basic conditions of (Goebel et al., 2012). In particular, we establish sufficient conditions for uniform asymptotic stability of a compact set based on some hierarchical stability assumptions involving two nested closed sets containing such a compact set. Moreover, mimickin...

‎This paper deals with the singular Sturm-Liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎Using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of Sturm-Liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

Hybrid systems which are capable of exhibiting simultaneously several kinds of dynamic behavior in different parts of a system (e.g., continuous-time dynamics, discrete-time dynamics, jump phenomena, switching and logic commands, and the like) are of great current interest. In the present paper we first formulate a model for hybrid dynamical systems which covers a very large class of systems an...

In this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperimetry in a general class of metric measure spaces. Let A be a family of subsets of a metric measure space (X, d, μ), with finite, unbounded volume. For t > 0, we define: I ↓ A(t) = inf A∈A,μ(A)≥t μ(∂A). We say that A is...