Pseudo Almost Periodic Solutions of Nonlinear Hyperbolic Equations with Piecewise Constant Argument

In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model for the dynamics of gas absorption,

ALMOST PERIODICITY AND EQUICONTINUITY OF THE TOPOLOGICAL TRANSFORMATION GROUP

In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.

Existence and global attractivity of unique positive almost periodic solution for a model of hematopoiesis

Sufficient conditions are obtained which guarantee the uniform persistence and global attractivity of solutions for the model of hematopoiesis. Then some criteria are established for the existence, uniqueness and global attractivity of almost periodic solutions of almost periodic system.

ALMOST PERIODIC SOLUTION OF ONE DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATION

This article studies one dimensional viscous Camassa-Holm equation with a periodic boundary condition. The existence of the almost periodic solution is investigated by using the Galerkin method.

Existence of asymptotically almost periodic solutions and stability properties for functional difference equations

For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.

Existence and Exponential Stability of Almost Periodic Solution for Hopfield Neural Network Equations with Almost Periodic Imput

By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.

Positive Almost Periodic Solution on a Nonlinear Logistic Biological Model with Grazing Rates

In this paper, we study the following nonlinear biological modeldx(t)/dt = x(t)[a(t)-b(t)x α (t)] + f(t, xt),by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived.

Existence and Uniqueness of Almost Periodic Solutions for Some Infinite Delay Integral Equations

In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.

The Existence of Periodic and Almost Periodic Solutions of Logistic Type Equation

In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a（t）, b（t） and e（t） are periodic functions, and this solution is an almost periodic solution if a（t）, b（t） and e（t） are almost periodic functions.

Existence and Uniqueness of Almost Periodic Solution for a Mathematical Model of Tumor Growth

This article is concerned with a mathematical model of tumor growth governed by 2nd order diffusion equation . The source of mitotic inhibitor is almost periodic and time-dependent within the tissue. The system is set up with the initial condition C(r, 0) = C0(r) and Robin type inhomogeneous boundary condition . Under certain conditions we show that there exists a unique solution for this model which is almost periodic.

APPROXIMATION OF SOLUTION OF LINEAR DIFFERENTIAL EQUATION WITH ALMOST PERIOD FUNCTION COEFFICIENTS

This paper is devoted to the study of approximation of the solution for the differential equation whose coefficients are almost period functions. To this end the authors establish the estimation of the solution of general linear differential equation for infinite interval case. For finite interval case, this equation was investigated by G. Tamarkin([1]) applying the Picard method of successive approximation.

Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Time-Varying Delays

In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.

The Almost Periodic Solution on a Lienard Equation

By using exponential dichotomies and Liapunov function method, we have studied the existence of almost periodic solutions on a Lienard system and have obtained some simple sufficient condition.

Weighted Pseudo Almost Periodic Solutions for a Class of Hematopoiesis Model with Time-Varying Delay

In this paper, firstly, a notion of a class of generalized weighted pseudo al- most periodic function is introduced, then we investigate some basic and essential properties of the space that consists of these functions. Finally, we study the exis- tence of weighted pseudo almost periodic solutions to hematopoiesis model with time- varying delay.

Pseudo Almost Periodic Solutions for Second Order Abstract Differential Equations

On the assumption that the Cauchy problem for incomplete second order abstract differential equation (u″(t)=Au(t), -∞ <t <∞) is well posed and the Cauchy problem for complete second order abstract differential equation ( u″(t)+A 1u′(t)+A 0u(t)=0, t≥0 ) is strongly well posed, the necessary conditions for their solutions to be pseudo almost periodic are derived.

Mean-square Almost Periodic Random Functions

In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.

Reducibility for a Class of Two-Dimensional almost Periodic System with Small Perturbation

This paper focuses on the reducibility of two-dimensional almost periodic system with small perturbation. We use the KAM iterative method to get the reducibility by an almost periodic transformation. The system has been reduced to a simple form. So we have dealt with the small perturbation problem of the almost periodic system.

New Results on Almost Periodic Solution of Shunting Inhibitory Cellular Neural Networks with Continuously Distributed Delays

In this paper,the existence,uniqueness and global attractivity are discussed on almost periodic solution of SICNNs（shunting inhibitory cellular neural networks）with continuously distributed delays.By using the fixed point theorem,differential inequality technique and Lyapunov functional method,giving the new ranges of parameters,several sufficient conditions are obtained to ensure the existence,uniqueness and global attractivity of almost periodic solution.Compared with the previous studies,our methods are more effective for almost periodic solution analysis of SICNNs with continuously distributed delays.Some existing results have been improved and extended.In order to show the effectiveness of the obtained results,an example is given in this paper.

Exponential Dichotomy and Eberlein-Weak Almost Periodic Solutions

We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.

Existence and Stability Property of Almost Periodic Solutions in Discrete Almost Periodic Systems

In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.