微分学中构造函数的新方法

结合实例将常微分方程中的首次积分和特征方程理论应用于微分学中函数的构造,从而使之有章可循.     

受迫二维广义KdV-Burgers方程的周期行波解

本文研究了受迫二维广义ＫｄＶ－Ｂｕｒｇｅｒｓ方程的周期行波解问题,讨论了解的有界性并给出了解的估计式,进而讨论了周期解的存在性及唯一性.     

抽象半线性发展方程正周期解的存在唯一性

讨论有序Banach空间E中半线性发展方程 u′(t)+Au(t)=f(t,u(t)),t∈R, ω-周期解的存在性,其中A为E中正C0-半群的生成元,f:R×E→E连续,关于t 以ω为周期．我们对相应的线性发展方程建立了周期解的存在唯一性,并对周期解算子的谱半径作了精确估计．借助于这个估计,我们用单调迭代方法获得了半线性发展方程正ω-周期解的存在唯一性．     

（2＋1）-DIMENSIONAL Tu HIERARCHY AND ITS INTEGRABLE COUPLINGS AS WELL AS THE MULTI-COMPONENT INTEGRABLE HIERARCHY

Under the frame of the(2 1)-dimensional zero curvature equation and Tu model,(2 1)-dimensional Tu hierarchy is obtained.Again by employing a subalgebra of the loop algebra ■_2 the integrable coupling system of the above hierarchy is presented.Finally,A multi-component integrable hierarchy is ob- tained by employing a multi-component loop algebra ■_M.     

Evolution of hypersurfaces by the mean curvature minus an external force field

In this paper, we study the evolution of hypersurface moving by the mean curvature minus an external force field. It is shown that the flow will blow up in a finite time if the mean curvature of the initial surface is larger than some constant depending on the boundness of derivatives of the external force field. For a linear force, we prove that the convexity of the hypersurface is preserved during the evolution and the flow has a unique smooth solution in any finite time and expands to infinity as the time tends to infinity if the initial curvature is smaller than the slope of the force.     

一类微分方程亚纯解的增长级

By meas of the Nevanlinna theory of the value distribution of meromorphic functions,this paper discusses the orders of growth of meromorphic solutions of differential equation and proves that the form of the solution is determined if the order are sufficiently large.     

基于$q$-差分Painlev\'e方程的几类$q$-差分方程解的性质

文章讨论了几类$q$-差分Painlev\''e方程的亚纯解性质,获得了方程亚纯解的存在性条件、增长级的估计,以及亚纯解$f$的$q$-差分$\Delta_qf(z):= f(qz)-f(z)$的极点收敛指数的估计等结果,进一步推广了Qi-Yang的结果.     

具有时滞的利率-流通量方程的建立及其应用

本文对金融网络建立了带有时滞的利率-流通量方程，应用时滞微分方程理论，我们得到金融网络中，各节点利率最终将稳定于其基本利率的充分必要条件；给出了各节点利率均振动的充分必要条件以及存在周期解的充分必要条件。     

三维全空间上Ginzburg Landau方程的整体吸引子

作者在三维全空间中考虑研究复Ginzburg Landau方程(CGL)的解的长时间行为。通过引入权空间，应用内插不等式和在权空间的先验估计，获得复 Ginzburg Landau方程整体解的存在性，进一步建立了整体吸引子的存在性。     

迭代微分方程解的存在性及分支

本文讨论迭代微分方程ｘ（ｔ）＝ｆ（ｘ（ｔ），ｘ（ｘ（ｔ）））的解的性态，并在ｆ（ｘ（ｔ），ｘ（ｘ（ｔ）））＝（ｘ＾２（ｔ）－μ）ｘ（ｘ（ｔ））时研究解的分支问题，更正了现有文献中的错误，结出了正确，完整的结果。