From an iteration formula to Poincaré's Isochronous Center Theorem for holomorphic vector fields

We first generalize a classical iteration formula for one variable holomorphic mappings to a formula for higher dimensional holomorphic mappings. Then, as an application, we give a short and intuitive proof of a classical theorem, due to H. Poincaré, for the condition under which a singularity of a holomorphic vector field is an isochronous center.

     

Parasite population delay model of malaria type with stochastic perturbation and environmental criterion for limitation of disease

We present a stochastic delay model of an infectious disease (malaria) transmitted by a vectors (mosquitoes) after an incubation time. A criterion for limitation of disease is found.     

Fixed point indices and invariant periodic sets of holomorphic systems

This note presents an intuitive method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will prove Needham's theorem in a more general version.

     

积分因子存在定理的一般充要条件

给出了积分因子存在的一般充分必要条件和计算公式.为寻找一阶微分方程的积分因子提供了一个一般方法.并举例说明定理的应用.     

A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL INEQUALITIES WITH DISTRIBUTED TYPE DEVIATING ARGUMENTS

ＡＣＬＡＳＳＯＦＳＥＣＯＮＤＯＲＤＥＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＩＮＥＱＵＡＬＩＴＩＥＳＷＩＴＨＤＩＳＴＲＩＢＵＴＥＤＴＹＰＥＤＥＶＩＡＴＩＮＧＡＲＧＵＭＥＮＴＳ（傅希林）￥ＦｕＸｉｌｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｈａｎｄｏｎｇＮｏｒ...     

一类常微分方程解的存在唯一性及其应用

提出并证明了一类常微分方程解的存在唯一性成立的一个充要条件,并给出了多项式形式增长函数的一列上界.最终将此结果应用到证明一类倒向随机微分方程的唯一解问题.     

关于两类二阶隐式常微分方程的解法

讨论就 y″解不出的二阶隐式常微分方程 x=f ( y′,y″)和 y′=f ( x,y″)的解法问题 .     

A functional partial differential equation arising in a cell growth model with dispersion

In this paper we solve an initial‐boundary value problem that involves a pde with a nonlocal term. The problem comes from a cell division model where the growth is assumed to be stochastic. The deterministic version of this problem yields a first‐order pde; the stochastic version yields a second‐order parabolic pde. There are no general methods for solving such problems even for the simplest cases owing to the nonlocal term. Although a solution method was devised for the simplest version of the first‐order case, the analysis does not readily extend to the second‐order case. We develop a method for solving the second‐order case and obtain the exact solution in a form that allows us to study the long time asymptotic behaviour of solutions and the impact of the dispersion term. We establish the existence of a large time attracting solution towards which solutions converge exponentially in time. The dispersion term does not appear in the exponential rate of convergence.     

Numerical solutions based on Chebyshev collocation method for singularly perturbed delay parabolic PDEs

The main purpose of this work is to provide a numerical approach for the delay partial differential equations based on a spectral collocation approach. In this research, a rigorous error analysis for the proposed method is provided. The effectiveness of this approach is illustrated by numerical experiments on two delay partial differential equations. Copyright © 2013 John Wiley & Sons, Ltd.     

Comment on “New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”

In this comment we analyze the paper [Abdelhalim Ebaid, S.M. Khaled, New types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity, J. Comput. Appl. Math. 235 (2011) 1984-1992]. Using the traveling wave, Ebaid and Khaled have found “new types of exact solutions for nonlinear Schrodinger equation with cubic nonlinearity”. We demonstrate that the authors studied the well-known nonlinear ordinary differential equation with the well-known general solution. We illustrate that Ebaid and Khaled have looked for some exact solution for the reduction of the nonlinear Schrodinger equation taking the general solution of the same equation into account.     

常系数线性差分方程的微分解法

用微分方法 ,解常系数线性差分方程     

The Oscillation of the Solutions of Higher-order Functional Differential Equations

In this paper we study the oscillation of the solutions of higher-order functional differential equations, and have given the new integral conditions when equation (1) is oscillatory and extended some known results.x(n)(t) p(t)x(g(t)) = 0, (1)where n is even number, p(t) ∈ C(R, [0, ∞)), g(t) ∈ C(R; R), g(t) f55 t,.     

方程f~（n）（x）＝Af~（n－k）（（ax＋b）／（cx－a））

本文提出方程ｆ~（ｎ）（ｘ）＝Ａｆ（ｎ－ｋ）（（ａｘ＋ｂ）／（ｃｘ－ａ）），证明它是可积的．所得结论是文献［１］中结论的推广．     

On Nonlinear Hyperbolic Functional Differential Equations

In this paper, existence of weak solutions of second order evolution equations is proved and some properties of the solutions are shown. The results are applied to higher order nonlinear hyperbolic functional differential equations.     

线性算子双半群及在间断和脉冲微分方程中的应用(英)

研究抽象Ｂａｎａｃｈ空间中线性微微分方程的可解性,利用算子双半群方法,讨论了在确定时间跳跃或脉冲的线性微分方程解的存在性,表明在一定条件下间断或脉冲方程的解存在唯一．     

The Loewner driving function of trajectory arcs of quadratic differentials

We obtain a first order differential equation for the driving function of the chordal Loewner differential equation in the case where the domain is slit by a curve which is a trajectory arc of a certain type of quadratic differential. In particular this includes the case when the curve is a path on the square, triangle or hexagonal lattice in the upper half-plane or, indeed, in any domain with boundary on the lattice. We also demonstrate how we use this to calculate the driving function numerically. Equivalent results for other variants of the Loewner differential equation are also obtained.