Hille and Nehari type criteria for third-order delay dynamic equations

The objective of this note is to present new Hille and Nehari type asymptotic criteria for a class of third-order delay dynamic equations on a time scale. Assumptions in our theorems are less restrictive, whereas the proofs are significantly simpler compared to those reported in the literature. The results obtained extend and improve some previous results.     

一类非线性差分方程正解的不存在性

本文研究一类非线性差分方程及其对偶方程,给出了方程不存在正解的充分条件,所得结论改进了[1]的结果。     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR A CLASS OF DELAY DIFFERENCE EQUATION

We propose a class of delay difference equation with piecewise constant nonlinearity. Such a delay difference equation can be regarded as the discrete analog of a differential equation. The convergence of solutions and the existence of asymptotically stable periodic solutions are investigated for such a class of difference equation.     

一类非线性波动方程弱解的存在唯一性

在考虑强阻尼效应的情形下,建立了一类轴向载荷作用下的波动方程.研究一类具有强阻尼的非线性波动方程的初边值问题的整体解的性态.以Sobolev空间的性质为工具,利用Faedo-Galerkin方法,证明了该方程在线性边界条件下弱解的存在唯一性,为力学中具有阻尼结构的振动问题的研究提供了重要依据.     

Pseudo-almost periodic solutions for abstract partial functional differential equations

In this work we study the existence and uniqueness of pseudo-almost periodic solutions for a first-order abstract functional differential equation with a linear part dominated by a Hille–Yosida type operator with a non-dense domain.     

Fite–Hille–Wintner-type oscillation criteria for second-order half-linear dynamic equations with deviating arguments

We study oscillatory behavior of solutions to a class of second-order half-linear dynamic equations with deviating arguments under the assumptions that allow applications to dynamic equations with delayed and advanced arguments. Several improved Fite–Hille–Wintner-type criteria are obtained that do not need some restrictive assumptions required in related results. Illustrative examples and conclusions are presented to show that these criteria are sharp for differential equations and provide sharper estimates for oscillation of corresponding $q$-difference equations.     

Oscillation and Nonoscillation Criteria for a Second Order Linear Equation

New oscillation and nonoscillation criteria are established for the equation

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATION

In this paper, a class of higher order linear differential equation is investigated. The order and the hyper-order of the solutions of the equation are exactly estimated under some certain conditions.     

APPLICATION OF THE G CLASS OF FUNCTIONS IN THE PARABOLIC CLASS

§1　IntroductionIn[1],wehaveintroducedtheconceptoftheGclassoffunctionsintheparabolicclass,andhaveprovedtheHldercontinuityofthiskindoffunctions.Theintroductionoftheconceptcontributestotheproofoftheregularityandexistenceofthesolutionforthefirstboundaryvalueproblemofparabolicequationindivergenceform.Here,weconsidertheapplicationsoftheGclassoffunctionsintheparabolicclasstothefirstboundaryvalueproblemofparabolicequation.Asweknow,ithasreceivedextensivestudyforthefirstboundaryvalueproblemofthefoll…     

高阶中立型时滞差分方程解的振动性

研究了一类具有变系数的高阶中立型时滞差分方程解的振动性，给出了其有界解振动的两个充分条件。     

具有可变时滞的非线性非自治差分方程的振动性及其应用

本文获得了一类具有可变时滞的非线性非自治差分方程的振动准则,建立了这类差分方程的几个线性化振动性定理,并得到了具有可变时滞的离散型非自治广义Logistic方程关于其正平衡点振动的一系列充分条件.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa^[6], G. Gundersen^[7] and J.K. Langley^[8], Li Chun-hong^[11].     

THE BOUNDARY VALUE PROBLEMS OF A CLASS OF ELLIPTIC EQUATION WITH A CURVE OF TURNING POINT

The boundary value problems of a class of elliptic equation with a curveof turning point are considered. Using the method of multiple scales and thecomparison theorem, the asymptotic behavior of solution for the boundary valueproblem is studied.     

ASYMPTOTIC BEHAVIOR OF POSITIVE RADIAL SOLUTIONS FOR THE GENERALIZED EMDEN-FOWLER EQUATION WITH APPLICATION

In this paper, we consider a class of semilinear parabolic differential equation where nonlinear term has local bounded coefficients. Under some assumptions, we get the existence and uniqueness of solution. Terminate to the time variable, we obtain the so called generalized Emden-Fowler equation and the asymptotic behavior of positive radial solutions have been given in all dimensions. At the end of this paper, we give its application to critical branching Brownian motion (also called measure-valued branching processes).     

关于一类二阶矩阵方程的敏度分析

In this paper, the sensitivity of the solution for a class of quadratic matrix equation which arises in the analysis of structural systems and vibration problems is discussed. With Brouwer fixed piont theory, the perturbation of the quadratic matrix equation is analyzed and two computational perturbation bounds are derived. Then a Rice condition number of some kind of solutions is given using the analytic expansion method. Two examples are presented in the last part.     

一类非线性Klein-Gordon方程的数值解

本文主要研究了一类非线性Klein-Gordon方程.利用Fourier谱方法对一类非线性Klein-Gordon方程的求解,给出了求解的离散过程,并通过了数值模拟与文献结果进行了对比.结果表明这种方法对于求解此类非线性Klein-Gordon方程具有很好的效果.     

一类时滞积分方程概周期解的存在性

本文讨论一类具广泛应用背景的概周期时滞积分方程,利用极限方程理论和不动点定理等方法,给出了关于概周期解的几个存在性定理.     

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF A CLASS OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY

The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.     

DECAYING SOLUTIONS OF NEUTRAL DIFFERENCE EQUATIONS WITH DELAYS

ＤＥＣＡＹＩＮＧＳＯＬＵＴＩＯＮＳＯＦＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＳ　ＷＩＴＨＤＥＬＡＹＳＸｉｅＳｈｅｎｇｌｉ（谢胜利）（ＪｉｎｚｈｏｕＴｅａｃｈｅｒ＇ｓＣｏｌｌｅｇｅ，湖北荆州师专，邮编：４３４１００）＆ＳｕｉＳｕｎＣｈｅｎｇ...     

关于一类代数微分方程的亚纯解的行为方式

本文的目的是研究了一类复代数微分方程的亚纯解增长性问题，将定理A推广到高阶方程。