在可交换四元数空间中的双曲方程的特征边值问题

讨论了一阶和二阶双曲复方程的特征边值问题.对其中两种线性方程,分别在不同的情况下获得通解和可解条件.而对于拟线性的二阶双曲复方程,证明了解的存在性和唯一性.     

一类两点边值问题的多重非负解

该文考虑两点边值问题[1/q(t)][q(t)y′(t)]′+p(t)f(y(t))= 0,λ_1 y(α)-λ_2y′(α)=0 and y(β)=B非负解的存在性, 其中p(t)可能在t=α或t=β附近具有奇异性, f(0)≥0, lim_(y→+∞)f(y)/y=+∞, 并且存在y>0, 使得f(y)<0.      

脉冲微分方程的上、下解及其在常微分方程上的应用

In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one solution for the problem. As an application, these results are applied to PBVP of ODE and some examples are given to illustrate our results.     

ON THE SINGULAR DIRECTIONS OF VALUE DISTRIBUTION OF HOLOMORPHIC CURVES IN P^n（C）

This article proves the existence of singular directions of value distribution theory for some transcendental holomorphic curves in the n-dimensional complex projective space Pn(C). An example is given to complement these results.     

Fourth-order problems with fully nonlinear boundary conditions

Differential inequality method, bounding function method and topological degree are applied to obtain the existence criterions of at least one solution for the general fourth-order differential equations under nonlinear boundary conditions, and many existing results are complemented.     

EFFICIENT SIXTH ORDER P-STABLE METHODS WITH MINIMAL LOCAL TRUNCATION ERROR FOR y"=f(x,y)

1. IntroductionWe consider a class of direct hybrid methods proposed in [11 for solving the second orderinitial value problemy" = f(t,y), y(0),y'(0) given (1.1)The basic method has the formandHere t. = nh and we define t.l.. = t. I aih, i = 1, 2 and n=0,1…     

High order generalized upwind schemes and numerical solution of singular perturbation problems

High even order generalizations of the traditional upwind method are introduced to solve second order ODE-BVPs without recasting the problem as a first order system. Both theoretical analysis and numerical comparison with central difference schemes of the same order show that these new methods may avoid typical oscillations and achieve high accuracy. Singular perturbation problems are taken into account to emphasize the main features of the proposed methods. AMS subject classification (2000)  65L10, 65L12, 65L50     

基于傅立叶变换轮廓术的物面相位提取

采用傅立叶变换轮廓术,针对基频提取的关键技术采用逐行傅立叶变换,准确提取基频信息的方法恢复相位信息.在此基础上,以未畸变条纹为基准,得出被测物体的真实位相值.该方法只需一幅条纹图,节约了测量时间.实验证明可实现无接触面型的自动传感.     

Positive solutions of singular boundary value problem of negative exponent Emden—Fowler equation

This paper investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar to standard Emden-Fowler equation. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as well as C¹[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem.     

Banach空间二阶周期边值问题解的存在性

利用一些比较结果，讨论了Banach空间中二阶周期边值问题解的存在性，获得了若干解的存在性与唯一性结果。