AN OSCILLATION CRITERION FOR SECOND ORDER SUBLINEAR DIFFERENTIAL EQUATIONS

ＡＮＯＳＣＩＬＬＡＴＩＯＮＣＲＩＴＥＲＩＯＮＦＯＲＳＥＣＯＮＤＯＲＤＥＲＳＵＢＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＬｉＷａｎｔｏｎｇ（ＺｈａｎｇｙｅＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，７３４０００）ＱｕａｎＨｏｎｇｓｈｕｎ（Ｌａｎｚ...     

HOMOCLINIC SOLUTIONS FOR A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL SYSTEMS

By means of an extension of Mawhin’s continuation theorem and some analysis methods, the existence of a set with 2kT-periodic solutions for a class of second order neutral functional differential syste...     

POSITIVE SOLUTIONS OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＯＦＮＥＵＴＲＡＬＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥（黄振勋，高国柱）ＨｕａｎｇＺｈｅｎｘｕｎ（Ｄｅｐｔ．ｏｆＭａｔｈｅｍａｔｉｃｓ，ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ２０...     

一类一阶泛函微分方程解的存在性与分支

本文研究方程ｘ’（ｔ）＝（ｘ２（ｔ）－μ）ｘ（ｘ（ｔ））μ≤０（１）解的性态。当μ＜０时，我们得到与Ｅｄｅｒ［１］和ｗａｎｇ［２］相类似的结论，也得到一些新的性质；当μ＝０时，我们得到全新的结论，证明方程（１）存在两端均不可延拓到∞的严格单调饱和强解，μ＝０是方程（１）的分支值。     

NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS

In this article, we describe on a state of the art of validated numerical computations for solutions of differential equations. A brief overview of the main techniques for self-validating numerics for initial and boundary value problems in ordinary and partial differential equations including eigenvalue problems will be presented. A fairly detailed introductions are given for the author's own method related to second-order elliptic boundary value problems. Many references which seem to be useful for readers are supplied at the end of the article.     

滞后型泛函微分方程的有界变差解

本文研究了一类滞后型泛函微分方程的有界变差解.利用Henstock-Kurzweil积分与Schauder不动点定理,在Henstock-Kurzweil积分下,得到了这类滞后型泛函微分方程有界变差解的存在性定理,推广了一些相关的结果.     

OSCILLATION AND EXISTENCE OF POSITIVE SOLUTIONS FOR NEUTRAL DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＡＮＤＥＸＩＳＴＥＮＣＥＯＦＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＳｈｅｎＪｉａｎｈｕａ（申建华）（ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，湖南师范大学，邮编４１００...     

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR INFINITE DELAY FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.     

广义泛函微分方程解的稳定性

本文首先给出广义泛函微分方程解的稳定性的概念,同时建立了有关稳定与不稳定的二个判据,然后作为例子,讨论二阶线性常系数广义微分差分程,得到了这类系统有关稳定与不稳定的若干结果,并发现了一些关于稳定性的分支或类似于分支的现象。     

ON THE GROWTH OF SOLUTIONS OF HIGHER-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS

Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.     

Regularization of nonlinear illposed problems with closed operators

In this paper Tikhonov regularization for nonlinear illposed problems is investigated. The regularization term is characterized by a closed linear operator, permitting seminorm regularization in applications. Results for existence, stability, convergence and con- vergence rates of the solution of the regularized problem in terms of the noise level are given. An illustrating example involving parameter estimation for a one dimensional stationary heat equation is given.     

ASYMPTOTIC BEHAVIOR FOR NONOSCILLATORY SOLUTIONS OF REACTION-DIFFUSION DIFFERENTIAL EQUATIONS WITH SEVERAL DELAYS IN THE NEUTRAL TERM

In this paper, we first consider differential equations with several delays inthe neutral term of the formstudy various cases of coefficients in the neutral term and obtain the asymptoticbehavior for nonoscillatory solution of (1~*) under some hypotheses. Moreover,we consider reaction-diffusion differential equations with several delays in theneutral term of the formfor (t, x)∈ R~+ ×Ω. We also study various cases of coefficients in the neutralterm and obtain the asymptotic behavior for nonoscillatory solution of (2~*)under some hypotheses.     

抽象半线性泛函微分方程正解的存在性

本文利用算子半群理论和锥压缩不动点定理 ,在合适的条件下建立了偏序 Banach空间中半线性泛函数微分方程全局正解的存在性     

非线性泛函微分方程解的性态

本文给出了一类非线性泛函微分方程解的性态的若干充要条件,推广了[1]的某些结论.     

一类中立型泛函微分方程周期解的存在性与唯一性

利用Schauder不动点理论,引入线性变换,用逆变换的思想,定性与定量地研究一类中立型泛函微分方程周期解的问题,获得了这一类泛函微分方程周期解存在性与唯一性的充分条件.我们的研究方法异于相关文献中常用的方法.     

SUFFICIENT CONDITIONS FOR THE EXISTENCE OF PERIODIC SOLUTIONS OF A AUTONOMOUS DIFFERENTIAL SYSTEM

ＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＳＦＯＲＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＡＡＵＴＯＮＯＭＯＵＳＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＨｕａｎｇＬｉｈｏｎｇ（黄立宏）ＹｕＪｉａｎｓｈｅ（庚建设）（Ｄｅｐａｒｔｍｅｎ...     

复微分方程组允许解的一个结果

本文利用亏量对复微分方程组的允许解的估计进行了改进，得到了一个主要结果。     

OSCILLATION THEOREMS FOR SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＪｉｎＭｉｎｇｚｈｏｎｇ（靳明忠）（ＷｕｈａｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ）Ａｂｓｔｒａｃｔ：Ｓｏｍ...     

ON THE BOUNDEDNESS CONDITIONS FOR SOLUTIONS OF A AUTONOMOUS DIFFERENTIAL SYSTEM

ＯＮＴＨＥＢＯＵＮＤＥＤＮＥＳＳＣＯＮＤＩＴＩＯＮＳＦＯＲＳＯＬＵＴＩＯＮＳＯＦＡＡＵＴＯＮＯＭＯＵＳＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭ￥ＨｕａｎｇＬｉｈｏｎｇ（黄立宏）；ＷａｎｇＺｈｉｃｈｅｎｇ（王志成）（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ，湖南大学...