NONLINEAR BOUNDARY VALUE PROBLEMS FOR FIRST ORDER DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS

The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equations with piecewise constant arguments.     

BOUNDARY VALUE PROBLEM FOR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATION

The author employs the method of upper and lower solutions together with the monotone iterative technique to obtain the existence theorem of minimal and maximal solutions for a boundary value problem of second order impulsive differential equation.     

一阶带参数的时滞微分方程的边值问题

本文利用上下解和单调迭代法，讨论了带参数的一阶时滞微分方程的边值问题，获得了这类问题极值解的存在性定理．     

TWO-POINT BOUNDARY VALUE PROBLEMS FOR A FIRST ORDER IMPLICIT DIFFERENTIAL EQUATIONS

1 Introduction and Main ResultInitial and periodic boundary value problems for the following first orderdifferential equationwhere f e C[[0, T] x R, R], have been studied for long by means of the monotone iterative technique (see, e.g. [1,2]). Recently, they have been investigatedagain by employing the method of generalized quasilinearization, a monotoneiterative technique (see [3-5]). However, more general two-point boundary value problems for a first order differential equation have not be…     

ANTI-PERIODIC BOUNDARY VALUE PROBLEM FOR FUNCTIONAL DIFFENERTIAL EQUATION

By using upper and lower solutions coupled with monotone iterative technique, we discuss the anti-periodic boundary value problem for first order functional diffenertial equation. A sufficient condition for the existence of the solution is obtained.     

PERIODIC BOUNDARY VALUE PROBLEMS FOR FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, we investigate the periodic boundary value problems for nonlinear first order functional differential equations. By establishing a new comparison result, criteria on the existence of maximal and minimal solutions are obtained.     

PERIODIC BOUNDARY VALUE PROBLEM FOR SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS

This paper investigates the periodic boundary value problems for a class of second order functional differential equations. The monotone iterative technique and the maximum principle are applied to obtain the existence of maximal and minimal solutions.     

一阶急式微分方程周期边值问题(英文)

本文我们描述了一个构造性方法．在存在一个上解β及下解α且α≤β情形下,得到两个单调序列一致收敛于如下周期边值问题．ｘ′（ｔ）＝ｆ（ｔ,ｘ（ｔ）,ｘ′（ｔ））,ｔ∈［０,Ｔ］ｘ（０）＝ｘ（Ｔ）,｛的极值解     

BOUNDARY VALUE PROBLEM FOR FIRST ORDER IMPULSIVE DIFFERENTIAL EQUATION WITH A PARAMETER AND INFINITE DELAY

In this paper, we consider a boundary problem of first order impulsive differential equation with a parameter and infinite delay. By using the method of upper and lower solutions, we get some sufficient conditions for the existence of its solutions.     

INTEGRAL BOUNDARY VALUE PROBLEM FOR FIRST ORDER IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS

By developing a comparison result and using the monotone iterative technique, we obtain the existence of the minimal and the maximal solutions to an integral boundary value problem for first order impulsive integro-differential equations.     

Banach空间中二阶非线性脉冲微分方程的Sturm-Liouville边值问题的极解

本文利用单调迭代技巧 ,锥理论和比较定理获得了Banach空间中二阶非线性脉冲微分方程的Sturm Liouville边值问题的极解     

THE PERIODIC BOUNDARY PROBLE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH VARIABLE TIME

1 IntroductionIt is well known that the monotonic iterative technique is a successfulmethod to obtain the extremal solutions of ODE or IDE with fixed time (see[IJ, [2]). Some results about the monotonic iterative technique for IDE withvariable time were obtained in the past few years (see [3--7]). Because thetheory of IDE with variable time is more complicated than that of IDE withfixed time, many authors considered the special case in which the pulse surfacet = T(x) is strictly monoton…     

SINGULAR PERTURBATION OF THREE-POINT BOUNDARY VALUE PROBLEM FOR THIRD ORDER DIFFERENTIAL EQUATIONS

In this paper, by the theory of differential inequalities, we study the existence and uniqueness of the solution to the three-point boundary value problem for third order differential equations. Furthermore we study the singular perturbation of three-point boundary value problem to third order quasilinear differential equations, construct the higher order asymptotic solution and get the error estimate of asymptotic solution and perturbed solution.     

奇异二阶泛函微分方程边值问题的多重正解

本文把ＺｈａｏｌｉＬｉｕ和Ｅｒｂｅ等人关于常微分方程边值问题多重正解的工作推广到二阶奇异混合型泛函微分方程边值问题,证明了所考虑的方程边值问题存在至少两个正解的充分条件。     

一阶隐式微分方程周期边值问题的上下解与迭合度

本文研究了一类一阶隐式微分方程周期边值问题的可解性.利用上下解方法和迭合度理论,获得了至少存在一个解的充分条件.     

BOUNDARY VALUE PROBLEMS FOR nTH ORDER RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS

1IntroductionTherearemanyresultsofstudyingboundaryvalueproblemsforsecondorderfunctionaldifferentialequations['I'].Butthestudyofboundaryvalueproblemsforhigherorderfunctionaldifferentialequationsrarelyappears.Inthispaper,wediscussthefollowingntypesofboundaryvalueproblemsforniborderfunctionaldifferentialequationswheref(t,yi,xo3xl)'',x.--1)isacontinuousrealfunctiondefinedonthesetA=[0,T]xCdxR.Forafixedr>0,letCrgC([--r,0],R)bethespaceofcontinuousfunctionon[--r,0]withthenormdefinedbyIIWll=supl…     

二阶奇异泛函微分方程的两点边值问题

本文研究具有Ｒｏｂｉｎ边界条件的二阶奇异泛函微分方程组Ａ（ｔ,ｘ,ｘ）ｘ＝ｆ（ｔ,ｘｔ,ｘｔ）的两点边值问题,给出该两点边值问题的两个解的先验估计定理和一个解的存在定理．     

MULTIPLE POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF DELAY DIFFERENTIAL EQUATIONS WITH DENUMBERABLE SINGULARITIES ON INFINITE INTERVAL

This paper deals with the existence of denumberable positive solutions to boundary value problems of delay differential equations with denumberable singularities on infinite intervals. By the fixed-point index theory and a new fixed-point theorem in cones, the existence of denumberable positive solutions is obtained under some suitable growth conditions imposed on the nonlinear term.     

非线性积分微分方程组奇摄动边值问题

本文讨论含积分算子的非线性微分方程组Ｒｏｂｉｎ边值问题的奇摄动,在适当假设条件下通过对角化技巧,利用逐步逼近法证明了解的存在,并得到直到Ｏ（ε＾Ｎ＋１）的按范数界限的一致有效估计。