This paper discusses a discrete multispecies Gilpin-Ayala mutualism system. We first study the permanence and global attractivity of the system. Assume that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive and uniformly asymptotically stable by constructing a suit...

The paper is concerned with conditions for the existence of almost periodic solutions of the following abstract functional differential equation u̇(t) = Au(t)+[Bu](t)+f(t), where A is a closed operator in a Banach space X, B is a general bounded linear operator in the function space of all X-valued bounded and uniformly continuous functions that satisfies a so-called autonomous condition. The ob...

In the present paper we prove an individual homogenization result for a class of almost periodic nonlinear parabolic operators. AMS Subject Classification (2000): 35B27, 35K55

This paper is devoted to the study of almost periodic solutions of a discrete two-species competitive system. With the help of the methods of the Lyapunov function, some analysis techniques, and preliminary lemmas, we establish a criterion for the existence, uniqueness, and uniformly asymptotic stability of positive almost periodic solution of the system. Numerical simulations are presented to ...

We summarize the conditions discovered for the existence of new ergodic type solutions (asymptotically almost periodic, pseudo almost periodic, . . .) of differential equations with piecewise constant arguments. Their existence is characterized by introducing a new tool, the ergodic sequences. 2000 Mathematics Subject Classification. 39-02, 34K14, 34D09.

We prove that every eigenvalue of a Schrbdinger operator with an almost periodic potential acting in the space of all square Haar-integrable functions on the Bohr compactification of ~ has multiplicity not greater than 2.

We introduce the group of exponents of a map of the reals into a metric space and give conditions under which this group embeds in the first Čech cohomology group of the closure of the image of the map. We show that this group generalizes the subgroup of the reals generated by the Fourier-Bohr exponents of an almost periodic orbit and that any minimal almost periodic flow in a complete metric s...

In this work, we study the existence of almost periodic solutions for some partial neutral functional differential equations. Using the variation of constants formula and the spectral decomposition of the phase space developed in [6], we prove that the existence of an almost periodic solution is equivalent to the existence of a bounded solution on R+.

Skew-product flow which is generated by a nonautonomous recurrent tridiagonal competitive-cooperative system of differential equations is considered. It is shown that any minimal set is an almost 1-1 extension of the base flow and any ω-limit set contains at most two minimal sets, which generalizes the results of J. Smillie [SIAM J. Math. Anal., 15(1984), pp. 530–534] in autonomous cases and H....

The Thue-Morse sequence is a classical example of an almost periodic (or uniformly recurrent) sequence in the sense that its associated symbolic dynamical system is minimal. We prove that the subsequence along squares of the Thue-Morse sequence is normal.