一类发展方程的混合方法

本文研究了一类发展方程的适定性问题和混合方法,征明了连续问题和离散问题解的存在唯一性,并对离散解作了误差估计.     

一类强阻尼非线性波动方程的广义解

用Galerkin方法研究了一类非线性波动方程的初边值问题,证明其在一定条件下强解的存在性.     

凸幂凝聚算子的不动点定理及其对抽象半线性发展方程的应用

从应用问题的需要出发,给出了一类新的算子-凸幂凝聚算子的定义,推广了凝聚算子的概念,并证明了这类新算子的不动点定理,从而推广了著名的Schauder不动点定理和Sadovskii不动点定理.作为应用,获得了Banach空间中一类具有非紧半群的半线性发展方程初值问题整体mild解和正mild解的存在性.     

非定常资产发展方程的最优控制分析

讨论了一类非定常非线性的资产发展方程中资产积累率的最优控制问题,利用泛函分析和积分方程理论,得到了最优解的存在唯一性.     

一个由四阶抛物方程支配的曲线流

本文研究了一类四阶曲线流,这个曲线流是一个描述人体血红细胞形状的泛函的梯度流.我们证明了对R2中任何光滑闭初始曲线,此流的光滑解长时间存在并且依子列收敛到泛函的一个临界点.     

带跳中立型随机发展方程解的逼近

在某个合适的Hilbert空间上建立一类由Poisson随机测度驱动的中立型随机发展方程mild解的存在唯一性. 进一步 , 采用Faedo-Galerkin方案对该解进行逼近.     

一类催化媒体中的超扩散

本文研究一类分形结构上超布朗运动的存在性.通过对特殊分形上布朗运动的转移密度的分析以及对一类微分方程解的存在性证明,得出了相应的超布朗运动的存在性.     

非线性群体发展方程的整体性态

本文研究一类非线性群体动力学模型,证明了C~1解的整体存在唯一性,并在特殊情形下讨论了解的渐近性态和平衡解的稳定性.     

一类特征值问题及其应用

研究一类特征值问题及其应用.首先应用常微分方程理论讨论一类边值问题非平凡解的存在唯一性,并将该研究结果应用到一类弹性系统的镇定问题.得到了系统渐近稳定的充分条件.     

二阶微分包含的边值问题及其应用

在Banach中讨论了一类二阶微分包含的边值问题和一类反馈控制问题.结合不动点定理,对解的存在性给出了两个充分性条件,最后应用前面的结果建立了反馈控制问题解的存在性定理.     

EXISTENCE AND UNIQUENESS OF STRONG PERIODIC SOLUTION OF THE EVOLUTION SYSTEM DESCRIBING GEOPHYSICAL FLOW—PART I： IN BOUNDED DOMAINS

61. IntroductionDiscovered by R. HideI3], the following evolution system has been used to describe thegeophysical flow:where u = u(xl,',XN,t) = (ul,',UN) and B = B(xl,',XN,t) = (BI,',BN) arethe velocity vectors Of Eulerian flow and magnetic fields respectively. p(x, t) and q(x, t) arepressures. j(x, t) and g(x,t) are volUme forces. p and u are the constants of density andviscosity of the flow respeCtively, p is the constant of magnetic permeability and A = f withelectrical resis…     

EXISTENCE AND UNIQUENESS OF STRONG PERIODIC SOLUTION OF THE EVOLUTION SYSTEM DESCRIBING GEOPHYSICAL FLOW|PART I: IN BOUNDED DOMAINS

The existence and uniqueness of a strong periodic solution of the evolution system describing geophysical flow in bounded domains of $R^N(N = 3,4)$ are proven if external forces are periodic in time and sufficiently small.     

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.     

On periodic solutions of countable systems of linear and quasilinear difference equations with periodic coefficients

We present conditions for the existence of periodic solutions of linear difference equations with periodic coefficients in spaces of bounded number sequences. In the case where the generating linear equation has a unique periodic solution, we indicate sufficient conditions for the existence of a periodic solution of a quasilinear difference equation.     

Global attractivity of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion

By employing the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion is established. Further, by constructing a Lyapunov functional and using the result of the existence of positive periodic solution, the attractivity of a positive periodic solution for above system is obtained.     

Periodic solutions for semi-linear evolution inclusions

In this paper, we study the periodic problem for semi-linear evolution inclusion. Using techniques from multivalued analysis and fixed point theorems, we establish existence theorems under the one-sided Lipschitz condition. First we prove existence theorems for nonconvex and convex problem. Second, we look for extremal periodic solutions and prove the relaxation theorem.     

Dynamic analysis of a turbidostat model with the feedback control

In this paper, a mathematical model with impulsive state feedback control is proposed for turbidostat system. The sufficient conditions of existence of positive order one periodic solution are obtained by using the existence criteria of periodic solution of a general planar impulsive autonomous system. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentration of microorganism and substrate. By investigating the periodic solution, the period and the initial point of the periodic solution are given. The results show that turbidostat with impulsive state feedback control tends to an order one periodic solution.     

Weighted pseudo-almost periodic solutions of a class of abstract differential equations

For abstract linear functional differential equations with a weighted pseudo-almost periodic forcing term, we prove that the existence of a bounded solution on R⁺ implies the existence of a weighted pseudo-almost periodic solution. Our results extend the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations. To illustrate the results, we consider the Lotka-Volterra model with diffusion.     

一类非线性微分方程渐近概周期解的存在性

利用函数的遍历性和耗散型条件,研究一类非线性微分方程渐近概周期解的存在性．在某些特定的条件下,得到了这类方程渐近概周期解存在性和唯一性结论．从而得到的结果在一定程度上推广和改进了相关结果．     

POSITIVE PERIODIC SOLUTION OF A PREDATOR-PREY SYSTEM WITH TIME DELAY

By using continuation theorem in coincidence degree theory,we study the existence of positive periodic solution for a delay and mutual interference predator- prey system with functional response,and obtain sufficient conditions for the existence of positive periodic solution.