Let {T (t)} t≥0 be a C-semigroup on a Banach space X with generator A. We will investigate the asymptotic almost periodicity of {T (t)} via the Hille-Yosida space of its generator.

In this note, we establish the existence of asymptotically almost periodic and almost periodic solutions for a class of partial integrodifferential equations.

A novel multiple scales method is formulated that can be applied to problems which have an almost periodic microstructure not in Cartesian coordinates but in a general curvilinear coordinate system. The method is applied to a model of the electrical activity of cardiac myocytes and used to derive a version of the bidomain equations describing the macroscopic electrical activity of cardiac tissu...

By means of the Cauchy matrix we give sufficient conditions for the existence and exponential stability of almost periodic solutions for the delay impulsive Lasota–Wazewska model. The impulses are realized at fixed moments of time.

This paper discusses a multispecies discrete Gilpin-Ayala mutualism system with feedback controls. We firstly obtain the permanence of the system. Assuming that the coefficients in the system are almost periodic positive sequences, we obtain the sufficient conditions for the existence of a unique almost periodic positive solution which is globally attractive.

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

In this paper, we consider the almost periodic solutions of a discrete cooperation system with feedback controls. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solution which is uniformly asymptotically stable. Keywords—Discrete cooperation model; Almost periodic solution; Feedback control; Lyapunov func...

We define, for a locally compact quantum group G in the sense of Kustermans– Vaes, the space of LUC (G) of left uniformly continuous elements in L∞(G). This definition covers both the usual left uniformly continuous functions on a locally compact group and Granirer’s uniformly continuous functionals on the Fourier algebra. We show that LUC (G) is an operator system containing the C∗-algebra C0(...

Consider the operator T = − d dx2 + x2 + q(x) in L2(R), where real functions q, q′ and ∫ x 0 q(s) ds are bounded. In particular, q is periodic or almost periodic. The spectrum of T is purely discrete and consists of the simple eigenvalues {μn}n=0, μn < μn+1. We determine their asymptotics μn = (2n+1)+(2π) −1 ∫ π −π q( √ 2n + 1 sin θ) dθ+O(n−1/3).