线性齐次微分方程的x^re^kx型解

线性齐次微分方程的ｘ~ｒｅ~（ｋｘ）型解周传忠，曾子平（华南师大５１０６３１）设。ｕ１，ｕ２……，ｕｍ是线性无关的２的函数组，ａｉｊ（ｉ＝０，１，……，ｎ；ｊ＝１，２，…，ｍ）都是常数，且ａｎ１，ａｎ２……，ａｎｍ不全为零．对于方程（１）ｉ＝０ｊ＝１的...     

Dissipation and Decay Estimates

We establish the optimal rates of decay estimates of global solutions of some abstract differentialequations,which include many partial differential equations.We provide a general treatment so that any futureproblem will enjoy the decay estimates displayed here as long as the general hypotheses are satisfied.Themain hypotheses are the existence of global solutions of the equations and some growth control of the Fouriertransform of the solutions.We establish the optimal rates of decay of the solutions for initial data in differentspaces.The main ingredients and technical tools are the Fourier splitting method,the iteration skill and theenergy estimates.     

Schauder不动点定理在脉冲微分方程解的存在性中的一个应用

本文用Ｓｃｈａｕｄｅｒ不动点定理证明了一类用上下解方法难以解决的脉冲微分方程边值问题解的存在性，改进现有的一些结果。     

中立型泛函微分方程与常微分方程解的渐近关系

本文讨论中立型泛函微分方程d/(dt)D(t,x_t)=A(t)x(t)+f(t,x_i)与常微分方程 (?)(t)=A(t)y(t)解的渐近等价性,以及中立型泛函微分方程d/(dt)D(t,x_t)=Ax(t)+f(t,x_i)与常系数常微分方程 (?)(t)=Ay(t)解的渐近增长关系。     

Submission of manuscripts

Annals of Differential Equations （Abbr： Ann. of Diff. Eqs.） is a specialized acade- mic journal, which is devoted to publishing research articles in the field of differential equations. The journal regularly covers topics such as the theory and applications of ordinary differential equations, functional differential equations, integral differential equations, stochastic differential equations, difference differential equations, numerical differential equations, boundary value problem, partial differential equations, bio-mathematics and differentiable dynamics.     

积分因子及其求法

微分方程：M（x，y）dx＋N（x，y）dy=0，若在单连通区域D内，M（x，y），N（x，y）有一阶连续偏导数，且满足则（1）为全微分方程，这时du=Mdx＋Ndy=0，得到（1）的通解为：u（x，y）=C。求全微分方程的通解，常用的有三种方法：1°，利用积分与路径无关，得出通解其中（X0，y0）是D内适当选定的点。2°，利用于得出通解”’”””如——”—”“”’a“””一”J””’”————叮3”，凑微方法。举例说明。＿。。。。＿＿，＿＿＿＿＿＿＿、吻，。。。、。一例1求微分方程（。osy＋cosx）甚一ysinx＋slny—0的通解。解将原方程改写…     

脉冲微分方程周期边值问题

脉冲微分方程周期边值问题董玉君，孙万凯（吉林大学数学研究所，长春１３００２３）（解放军农牧大学数学教研室，长春１３００６２）１引言本文研究脉冲微分方程周期边值问题这里ｉ＝１，２，…，ｎ，ｋ＝１，２，…，ｐ，ｎ和ｐ是自然数，ｔｋ∈（ａ，ｂ）满足ａ＝ｔｏ...     

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.     

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

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

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.     

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.