带梯度算子二阶方程的渐近概周期解

利用渐近概周期函数的性质得到带梯度算子二阶方程的渐近概周期解在C（R^-）中的存在性．同时利用迭代法和线性常微分方程的概周期解的存在性和唯一性,得到R上此方程渐近概周期解的存在和唯一性．     

Note on periodic solutions of fractional differential equations

The existence and nonexistence of periodic solutions are discussed for fractional differential equations by varying the lower limits of Caputo derivatives. The developed approach is illustrated on several examples.     

逐段常变量微分方程组概周期型解存在唯一性

通过差分方程指数二分法,我们研究了一类具有变系数逐段常变量微分方程组概周期与伪概周期解的存在唯一性与渐近稳定性,改进了已有文献的结果,并且得到了差分方程满足指数二分性的一个充分条件．     

一类非线性泛函微分系统的概周期解

结合应用指数型二分性原理和Schaefer定理,考虑了一类完全非线性泛函微分方程概周期解的存在性问题,改善和推广了已有的结果.并将获得的结果推广到周期系统,获得了一些新的结果.     

一类一阶和二阶微分方程的渐近概周期解

对于一阶微分系统u′+F(u)=h(t),其中F为R~n上的严格单调算子,本文给出了其渐近概周期解存在和唯一的一个充分条件和一个必要条件.特别,对于一阶微分系统u′+▽Φ(u)=h(t),其中▽Φ代表R~N上凸函数Φ的梯度,讨论了其渐近概周期解存在和唯一的充分必要条件,并且把一些结果推广到了一类二阶方程.     

Recurrent solutions of the derivative Ginzburg–Landau equation with boundary forces

In this paper, we will establish the existence of the bounded solutions, periodic solutions, quasi-periodic solutions and almost periodic solutions for the derivative Ginzburg–Landau equation with time-dependent boundary external forces. A smoothing effect for the semigroup associated with linear Ginzburg–Landau operator is the crucial tool in establishing the main results.     

Periodic solutions of conservation laws constructed through Glimm scheme

We present a periodic version of the Glimm scheme applicable to special classes of systems for which a simplication first noticed by Nishida (1968) and further extended by Bakhvalov (1970) and DiPerna (1973) is available. For these special classes of systems of conservation laws the simplification of the Glimm scheme gives global existence of solutions of the Cauchy problem with large initial data in , for Bakhvalov's class, and in , in the case of DiPerna's class. It may also happen that the system is in Bakhvalov's class only at a neighboorhood of a constant state, as it was proved for the isentropic gas dynamics by DiPerna (1973), in which case the initial data is taken in with , for some constant which is for the isentropic gas dynamics systems. For periodic initial data, our periodic formulation establishes that the periodic solutions so constructed, , are uniformly bounded in , for all 0$">, where is the period. We then obtain the asymptotic decay of these solutions by applying a theorem of Chen and Frid in (1999) combined with a compactness theorem of DiPerna in (1983). The question about the decay of Nishida's solution was proposed by Glimm and Lax in (1970) and has remained open since then. The classes considered include the -systems with , , , which, for , model isentropic gas dynamics in Lagrangian coordinates.

     

Recurrent solutions of the linearly coupled complex cubic‐quintic Ginzburg‐Landau equations

In this paper, we will establish the bounded solutions, periodic solutions, quasiperiodic solutions, almost periodic solutions, and almost automorphic solutions for linearly coupled complex cubic‐quintic Ginzburg‐Landau equations, under suitable conditions. The main difficulty is the nonlinear terms in the equations that are not Lipschitz‐continuity, traditional methods cannot deal with the difficulty in our problem. We overcome this difficulty by the Galerkin approach, energy estimate method, and refined inequality technique.     

具有阶段结构且食饵有避难所的模型分析

研究了捕食者具有阶段结构且食饵有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下存在唯一全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.     

Dynamic analysis of a non-autonomous ratio-dependent predator-prey model with additional food

In this paper, a non-autonomous ratio-dependent three species predator-prey system with additional food to top predator was proposed. The permanence of the model is obtained. Based on the continuation theorem, the sufficient conditions for the existence of a periodic solution are obtained. By using the method of Lyapunov function, we prove that the system exists a unique positive almost periodic solution under some certain conditions.     

Characterization of equilibrium strategies in a class of difference games

We formulate a class of N player difference games and derive open—loop and Markov equilibria. It turns out that both types of equilibria can be characterized by a set of difference equations that describe the equilibrium dynamics. We analyze the stability properties of the difference equations that correspond to an equilibrium and find that in both the open—loop and the Markov game there is convergence towards a steady state equilibrium     

无穷时滞Liénard方程的周期解

讨论具有无穷时滞Liénard型方程x+э2F(x)/эx2x+g(t,xt)=p(t)的周期解问题,利用重合度理论得到了周期解存在的充分条件.     

Bounded and almost periodic solutions of convex Lagrangian systems

We study some properties of bounded and almost periodic solutions of convex Lagrangian systems in the presence of almost periodic forcing

     

Almost periodic linear differential equations with non-separated solutions

A celebrated result by Favard states that, for certain almost periodic linear differential systems, the existence of a bounded solution implies the existence of an almost periodic solution. A key assumption in this result is the separation among bounded solutions. Here we prove a theorem of anti-Favard type: if there are bounded solutions which are non-separated (in a strong sense) sometimes almost periodic solutions do not exist. Strongly non-separated solutions appear when the associated homogeneous system has homoclinic solutions. This point of view unifies two fascinating examples by Zhikov-Levitan and Johnson for the scalar case. Our construction uses the ideas of Zhikov-Levitan together with the theory of characters in topological groups.     

Unbounded solutions and periodic solutions for second order differential equations with asymmetric nonlinearity

In this paper we will prove the coexistence of unbounded solutions and periodic solutions for the asymmetric oscillator

where and are positive constants satisfying the nonresonant condition

and is periodic in the first variable and bounded.

     

Time periodic and almost time periodic solutions to rotating stratified fluids subject to large forces

Consider the 3D incompressible Boussinesq equations for rotating stably stratified fluids. It is shown that this set of equations possesses a unique time periodic or almost time periodic solutions for external forces satisfying these properties, which, however, do not necessarily need to be small. An explicit bound on the size of the external force, depending on the buoyancy frequency N, is given, which then allows for the unique existence of time periodic or almost periodic solutions. In particular, the size of the external forces can be taken large with respect to the buoyancy frequency. The approach depends crucially on the dispersive effect of the rotation and the stable stratification.     

PERIODIC AND ALMOST PERIODIC SOLUTIONS OF A CERTAIN INFINITE DELAY INTEGRAL EQUATION

In this paper,by using successive approximation method and fixed-point theorem,we discuss a class of infinite delay integral equation and obtain some sufficient conditions which guarantee the existence and uniqueness of the peri- odic and almost periodic solutions of the system.     

ALMOST PERIODIC SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

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