一致渐近稳定和周期解、概周期解的存在性

本文建立了系统解一致稳定、解一致渐近稳定和某种Liapunov函数存在的充要条件,并且得到:满足Lipschitz条件而且解一致渐近稳定的概周期系统有唯一的概周期解,周期系统有唯一的周期解。     

常微分方程解的存在区间和周期解

讨论解的存在区间,说明周期函数如何是周期解以及它和Poincaré映射的关系.对周期的Riccati方程研究了周期解的个数,是文[8]中的定理1的一个补充,同时也研究了周期捕获的人口方程解的存在区间和周期解问题.     

一类时滞微分系统的周期解

研究了一类具分布时滞的一阶微分系统的周期解的存在性和全局吸引性.先通过利用重合度理论中的Mawhin延拓定理讨论了周期解的存在性,建立了一些判断准则;进而通过构造适当的Lyapunov泛函以及周期解的存在性结果研究了该类时滞微分系统的周期解的全局吸引性,获得了保证其周期解全局吸引的充分性条件.     

强平均解与概周期解的存在性

本文定义了概周期微分方程的强平均解,利用强平均解的性质,讨论了强平均解与概周期解的关系,从而建立了概周期解存在的若干定理。     

具有Monod-Haldane功能反应和脉冲效应的捕食系统的动力学性质

基于综合害虫防治,对具脉冲效应的Monod—Haldane功能反应的捕食系统进行了分析,根据Floquet乘子理论,获得了害虫灭绝周期解全局渐近稳定与系统持续生存的条件．并讨论了害虫灭绝周期解附近分支出非平凡周期解的问题,且文章利用Matlab软件对害虫灭绝周期解害虫周期爆发现象进行了数值模拟．     

共振条件下一类方程无界解和周期解的共存性

讨论了在共振条件下一类具有等时位势的方程无界解和周期解的共存性．利用Poincare映射轨道的性质,给出了无界解的存在性条件．在此条件下,Poincare-Bohl定理,得到了方程的一个周期解,进而说明共振条件下这类方程无界解和周期解的是可以共存的．最后,给出了一个无界解和周期解共存的具有等时位势的方程实例．     

一类n维中立型泛函微分方程的周期解

通过对NFDE周期系统；周期解的讨论，给出了其周期解界的估计式，结合不动点原理研究了下列系统：周期解的存在性，唯一性等问题，得到一些新的结果．     

磁流体方程的时间解析性和时间周期解

考查了周期边界条件下的磁流体方程,证明了它的解关于时间是解析的,由此得到了磁流体方程的解的向后惟一性.对于周期解,证明了当周期小于某个常数时,周期的弱解是强解,进一步地这样的强解是定常解.     

不动点理论与里卡提方程两个正周期解的存在性

利用压缩映射原理,得到里卡提方程一个正周期解的存在性;利用变量变换方法,将里卡提方程转化为伯努利方程.根据伯努利方程的周期解和变量变换,得到里卡提方程的另一个周期解.并讨论了两个正周期解的稳定性,一个周期解在某个区间上是吸引的,另一个周期解在R上是不稳定的.     

关于退化中立型微分方程的周期解

讨论了退化中立型微分方程的周期解问题,给出了周期解存在性的条件和二维退化中立型微分方程周期解存在的代数判据,并且举例说明了其应用.     

Existence of solutions of non-autonomous second order functional differential equations with infinite delay

In this paper the existence of solutions of a non-autonomous abstract retarded functional differential equation of second order with infinite delay is considered. Assuming the existence of an evolution operator corresponding to the associate abstract Cauchy problem of second order, we establish the existence of mild solutions of the functional equation. Furthermore, we study the existence of classical solutions of the abstract Cauchy problem of second order and we apply these results to establish the existence of classical solutions of the functional equation. Finally, we apply our results to study the existence of solutions of the non-autonomous wave equation with delay.     

Existence of solutions of the nonautonomous abstract Cauchy problem of second order

In this paper the existence of solutions of a nonautonomous abstract Cauchy problem of second order is considered. Assuming appropriate conditions on the operator of the equation, we establish the existence of mild solutions and, in some cases, we construct an evolution operator associated to the homogeneous equation. Using this evolution operator we obtain existence of solutions for the inhomogeneous equation. Finally, we apply our results to study the existence of solutions of the nonautonomous wave equation.     

On the Stochastic Wave Equation with Nonlinear Damping

We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping.     

耗散Camassa-Holm方程的吸引子

本文就一个新的色散水波方程Camassa-Hohn方程的动力学行为进行了研究，讨论了耗散CH方程的解的整体存在，获得了其解半群在H^2中全局吸引子的存在性．     

Optimal control of the viscous Dullin–Gottwalld–Holm equation

This paper studies the problem for optimal control of the viscous DGH equation. The existence and uniqueness of weak solution to the equation are proved in a short interval. The optimal control of the viscous DGH equation under boundary condition is given and the existence of optimal solution to the equation is proved.     

一类共形不变摄动积分方程正解的存在性

本文讨论了一类共形不变摄动积分方程正解的存在性. 我们证明了:当参数对(p, q) 属于集合(-n, 0) × (0,∞) 且pq + p + 2n = 0 时, 对应摄动积分方程存在正解; 而当参数对(p, q) 属于集合(0,∞)×(-∞, 0) 也满足pq +p+2n = 0 时, 摄动积分方程不存在非负解. 这与原共形不变积分方程有着本质的不同, 此结果隐含着这类积分方程正解的存在性取决于解在无穷远处的性态.     

The attractor for the two-dimensional weakly damped KdV equation in belt field

This paper aims at presenting a proof of the existence of the attractor for the two-dimensional weakly damped KdV equations in belt field. By using the Bourgain spaces and the orthogonal projection, we prove the existence of the attractor for the reduced equation which is obtained from the two-dimensional weakly damped KdV equation in belt field. By using the time estimate of the blow-up of the KdV equation, we get the compact and bounded aborting set and prove the existence of the attractor for the two-dimensional weakly damped KdV equation in belt field.     

A Generalization of a Volterra Integral Equation

Sufficient conditions for the existence of a solution to a non-linear Volterra integral equation are given for special cases of the general equation. In the generality given here, this equation has, apparently, not been studied before. The major technique used is the classical fixed point theorem of Banach. An apparent innovation of this article is the use of Banach's theorem to prove both the existence and find the location of a solution to the integral equation and prove the existence and find the location of the derivative to this solution, which exists almost everywhere. Furthermore, it is shown that for some particular choices of the constants, multiple solutions exist to this equation.     

On asymptotic behavior of solutions to Korteweg-de Vries type equations related to vortex filament with axial flow

We study the global existence and asymptotic behavior in time of solutions to the Korteweg-de Vries type equation called as “Hirota” equation. This equation is a mixture of cubic nonlinear Schrödinger equation and modified Korteweg-de Vries equation. We show the unique existence of the solution for this equation which tends to the given “modified” free profile by using the two asymptotic formulae for some oscillatory integrals.     

广义神经传播方程的整体吸引子

使用Galerkin方法,结合Sobolev空间理论和不等式技巧,给出了广义神经传播方程解的存在唯一性定理,然后利用吸引子存在性定理,采用半群方法证明了方程整体吸引子的存在性.