亚纯函数系数微分方程的解和小函数的关系

研究了一类亚纯函数为系数的二阶非齐次线性微分方程的解及其微分多项式和小函数的关系,并得到了这类微分方程解以及解的一阶,二阶导数与微分多项式的不动点性质.     

慢增长系数微分方程的解及其导数的不动点

运用值分布理论研究了高阶慢增长系数线性微分方程的解及其导数的不动点问题.当存在某个系数对方程的解的性质起主要支配作用时,得到了方程解及其导数的不动点收敛指数的精确估计,推广了有关文献中的结论.     

二阶复域微分方程亚纯解的不动点与超级

研究了亚纯函数系数的二阶线性微分方程解的不动点及超级问题,得到了有关复域微分方程亚纯解的不动点性质,并且由于受到微分方程的制约,其性质与一般亚纯函数的不动点性质相比,显得十分有趣.     

二阶复域微分方程解的不动点与超级

文中首次研究了４种类型的整函数系数的二阶线性微分方程的解的不动点及超级问题,得到：复域微分方程解的不动点性质,由于受到微分方程的制约,与一般超越整函数的不动点性质相比,是十分有趣的．     

一类微分方程的解及其解的导数与不动点的关系

研究了一类亚纯系数微分方程的复振问题,通过应用亚纯函数的分解和模的增长估计,得到了该类方程的级的精确估计,同时对方程的解及其一阶导数与不动点间的关系进行了研究,指出由于受到微分方程的制约,该类方程的不动点密度与解的增长性有着密切的关系.     

Fixed Points and Hyper Order of Differential Polynomials Generated by Solutions of Differential Equation

This article studies the problem on the fixed points and hyper-order of differential polynomials generated by solutions of two type of second order differential equations. Because of the control of differential equation, we can obtain some precise estimates of their hyper-order and fixed points.     

关于二阶复微分方程解的幂和解的微分多项式的不动点

本文研究了以整函数为系数的二阶线性微分方程解的幂和解生成的微分多项式的不动点问题,得到:二阶线性微分方程解生成的微分多项式的不动点性质,由于受到微分方程的限制,与一般亚纯函数的不动点性质相比是十分有趣的.事实上,它们与解的增长性密切相关.     

亚纯函数系数高阶复域微分方程解的不动点

研究了一类亚纯函数系数的高阶线性微分方程的解的不动点问题,应用值分布的理论和方法,得到了复域微分方程亚纯解的不动点性质.     

二阶线性微分方程亚纯解的不动点与超级

本文研究了以亚纯函数为系数的二阶线性微分方程的解及其一阶和二阶导数的不动点及超级问题，得到：二阶线性微分方程亚纯解及其一阶和二阶导数的不动点性质，由于受到微分方程的限制，与一般亚纯函数的不动点性质相比是十分有趣的，事实上，它们与解的增长性密切相关。     

A parameter study of epitaxial crystal growth

A third order autonomous ordinary differential equation is studied that is derived from a mathematical model of epitaxial crystal growth on misoriented crystal substrates. The solutions of the ODE correspond to the traveling wave solutions of a nonlinear partial differential equation which is related to the Kuramoto–Sivashinsky equation. The fixed points, the periodic solutions, and the heteroclinic orbits of the ODE are analysed, and stability results are given. A variety of nonlinear phenomena are observed, including Gavrilov–Guckenheimer bifurcations, homoclinic bifurcations, and a cascade of period doublings.     

Differential polynomials generated by linear differential equations

This article is devoted to considering value distribution theory of differential polynomials generated by solutions of linear differential equations in the complex plane. In particular, we consider normalized second-order differential equations f″+A(z)f=0, where A(z) is entire. Most of our results are treating the growth of such differential polynomials and the frequency of their fixed points, in the sense of iterated order.     

奇异四阶两点边值问题的正解

本文研究了四阶奇异边值问题正解的存在性，昕用方法是锥不动点定理，Arzela-Ascoli定理及解的先验估计．     

一类无穷多点边值问题正解的存在性

研究一类二阶非线性常微分方程无穷多点边值问题正解的存在性,利用不动点指数理论得到了方程至少存在一个正解的若干充分条件.     

An entire function and its derivatives sharing a polynomial

In this paper, we study the growth of solutions of a first-order linear differential equation and that of a second-order linear differential equation. From this we obtain some uniqueness theorems of a nonconstant entire function and its first derivative having the same fixed points with the same multiplicities. The results in this paper also improve some known results. Some examples show that the results in this paper are best possible.     

Bifurcations of hyperbolic fixed points for explicit Runge-Kutta methods

Discretization of autonomous ordinary differential equationsby numerical methods might, for certain step sizes, generatesolution sequences not corresponding to the underlying flow—so-called‘spurious solutions’ or ‘ghost solutions’.In this paper we explain this phenomenon for the case of explicitRunge-Kutta methods by application of bifurcation theory fordiscrete dynamical systems. An important tool in our analysisis the domain of absolute stability, resulting from the applicationof the method to a linear test problem. We show that hyperbolicfixed points of the (nonlinear) differential equation are inheritedby the difference scheme induced by the numerical method whilethe stability type of these inherited genuine fixed points iscompletely determined by the method's domain of absolute stability.We prove that, for small step sizes, the inherited fixed pointsexhibit the correct stability type, and we compute the correspondinglimit step size. Moreover, we show in which way the bifurcationsoccurring at the limit step size are connected to the valuesof the stability function on the boundary of the domain of absolutestability, where we pay special attention to bifurcations leadingto spurious solutions. In order to explain a certain kind ofspurious fixed points which are not connected to the set ofgenuine fixed points, we interprete the domain of absolute stabilityas a Mandeibrot set and generalize this approach to nonlinearproblems.     

Existence and Uniqueness of Fixed Points for Mixed Monotone Operators with Application

In this paper, a class of mixed monotone operators is studied. Some new fixed point theorems are presented by means of partial order theory, and the uniqueness and existence of fixed points are obtained without assuming the operator to be compact or continuous. Our conclusions extend the relevant results. Moreover,as an application of our result, the existence and uniqueness of positive solution for a class of fractional differential equation boundary value problem are proved.     

Characterization of the finite weak singularities of quadratic systems via invariant theory

This article is about weak singularities of quadratic differential systems, that is, non-degenerate singular points with traces of the corresponding linearized systems at such points equal to zero. These could be foci, centers or saddles. Necessary and sufficient conditions for a real quadratic system to possess a fixed number of weak singularities of a specific order are given. The conditions are stated in terms of affine invariant polynomials in the 12-dimensional space of the coefficients.     

Example of a suspension bridge ODE model exhibiting chaotic dynamics: A topological approach

Using an elementary phase-plane analysis combined with some recent results on topological horseshoes and fixed points for planar maps, we prove the existence of infinitely many periodic solutions as well as the presence of chaotic dynamics for a simple second order nonlinear ordinary differential equation arising in the study of Lazer-McKenna suspension bridges model.     

Global stability of discrete-time competitive population models

We develop practical tests for the global asymptotic stability of interior fixed points for discrete-time competitive population models. Our method constitutes the extension to maps of the Split Lyapunov method developed for differential equations. We give ecologically-motivated sufficient conditions for global stability of an interior fixed point of a map of Kolmogorov form. We introduce the concept of a principal reproductive mode, which is linked to a normal at the interior fixed point of a hypersurface of vanishing weighted-average growth. Our method is applied to establish new global stability results for 3-species competitive systems of May-Leonard type, where previously only parameter values for local stability was known.     

无穷区间上二阶奇异微分方程三点边值问题正解的存在性

讨论了一类无穷区间上二阶奇异微分方程三点边值问题正解的存在性和唯一性.通过应用对角延拓原理,不动点指标理论和不等式技巧,得到了该类边值问题正解存在性和唯一性的充分条件,允许非线性项有奇性.