泛函微分方程是数学学科中的一个重要分支。
Functional differential equations is an important branch in the theory of mathematics.
本文给出一类双曲偏泛函微分方程解的振动准则。
In this paper, oscillation criteria of solutions for a certain partial functional differential equations are obtained.
动力系统的许多问题都可以化为迭代泛函微分方程。
Many problems of dynamical systems can be reduced to an iterative functional differential equation.
对迭代动力系统的研究必然涉及迭代泛函微分方程问题。
The study of iterative dynamical systems involves iterative functional differential equations.
第一章，建立了伊藤随机泛函微分方程的一些基本定理。
In Chapter 1, some basic theories of stochastic functional differential equations of Ito-type are developed.
本文研究一类非线性抛物型偏泛函微分方程的渐近行为。
This paper is devoted to the investigation of the asymptotic behavior for a class of nonlinear parabolic partial functional differential equations.
本文研究分段常数变量线性中立型泛函微分方程的振动性。
In this paper, we consider the oscillatory properties of neutral linear variable functional differential equation with piecewise constant delays.
中立型泛函微分方程的振动性在理论和应用中有着重要意义。
The oscillation of neutral functional differential equations has important implications in both theory and application.
研究了一类非线性滞后型泛函微分方程周期解的存在性问题。
The existence problem for a class of nonlinear retarded functional differential equation is researched.
因此对泛函微分方程的研究，不但有重要的理论价值，而且有实用价值。
Therefore, it is of great theoretical and practical value to research functional differential equations.
讨论了一类二阶非线性泛函微分方程的振动性，得到一些新的振动准则。
The oscillation of a class of second-order nonlinear functional differential equations is discussed, and some new oscillation criteria for the equations are obtained.
目的研究一类具有连续偏差变元的双曲偏泛函微分方程边值问题解的振动性。
Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments.
通过建立泛函微分不等式，研究了一类高阶中立型偏泛函微分方程解的振动性。
By establishing a functional differential inequality, some sufficient conditions are obtained for the oscillation of solutions of certain partial functional differential equations.
其次，利用随机分析技巧和拟有界条件，建立了伊藤随机泛函微分方程解的延拓定理；
Furthermore, a continuation theorem for stochastic functional differential equations of Ito-type is given by using stochastic analysis technique and the quasi-boundedness condition.
该文获得了一类具有连续偏差变元的二阶非线性偏泛函微分方程的振动性的充分性条件。
In this paper, we study a class of boundary value problems of even order nonlinear neutral partial functional differential equations with continuous distribution delay.
本文研究一阶非线性中立型泛函微分方程的振动性。得到了该方程振动的充分性判别法则。
This paper deals with the oscillation of the first order nonlinear neutral type functional differential equation, and obtains sufficient criterion of the equation oscillation.
本文讨论一类三阶时滞泛函微分方程解的渐近性质，给出了若干解的有界性及解趋于零的判定准则。
Som criteria on the asymptotic behavior (such as boundness, tending to zero) of solutions for a kind of third order delay functional differential equation are established.
偏泛函微分方程来源于物理学、生物学、工程学等学科领域中众多的数学模型，具有强烈的实际背景。
Partial functional differential equations come from many mathematical models in physics, biology, engineering and other fields, which have strongly practical background.
研究了一类中立型双曲型泛函微分方程边值问题，得到了判定解是振动的新的方法，推广了已有的结果。
In this paper the boundary value problem for a neutral hyperbolic differential equation is studied. A new method for judgement of oscillation solution is obtained and is spreded known results.
利用李雅普·诺夫泛函研究中立型泛函微分方程的概周期解的存在性，其中李雅普·诺夫泛函不是正定的。
We investigate the existence of almost periodic solutions of functional differential equations of neutral type by Liapunov functional which is not positive definite.
因此，非常有必要对随机泛函微分包含解的存在性，可控性和泛函微分方程周期解的存在性问题进行研究。
It is necessary for us to study the existence and controllability of the solution of stochastic differential inclusions and the existence of periodic solutions for functional differential equations.
研究一类具有连续分布滞量的偶数阶非线性中立型泛函微分方程解的振动性，得到了该类方程的若干新的振动准则。
We study the oscillation of solutions for a class of even order nonlinear neutral functional differential equations with continuous distributed delay.
本文研究了一类具有连续偏差变元带中立项的双曲偏泛函微分方程解的H-振动性，给出了判别解H-振动的充分条件。
This paper studies the H-oscillations of hyperbolic partial functional in differential equations with deviating arguments and provides it with sufficient conditions.
本文应用比较方法，提出滞后型泛函微分方程初始问题的近似解法，给出了解的近似迭代序列及其误差估计式，并证明迭代序列的收敛性和计算稳定性。
Using the comparison method, an approximate approach to the delay-differential equations is proposed in this paper. The proof of its convergence and calculation stability is also given.
本文证明了关于对称泛函临界点的一个定理并用以研究非线性椭园型偏微分方程的多重解。
In this paper we prove a theorem for the critical points of symmetric functionals through which we research the multiple solutions of nonlinear elliptic PDE.
用泛函的方法研究一类二阶微分方程周期解的存在性。
We studied a class of two order differential equations by means of the functional method.
应用非线性泛函分析的理论和方法研究了一类二阶线性微分方程，证明了周期衰减解的存在性。
The second-order nonlinear differential equations are studied and the existence of the periodic degenerate solution is proved with the principle of the functional analysis.
图像的卡通部分是由一个有界变差(BV)函数来刻画，相应的将BV罚项合并到变分泛函中需要解偏微分方程。
The cartoon component of an image is modeled by a bounded variation (BV) function; the corresponding incorporation of BV penalty terms in the variational functional leads to solve PDE equations.
图像的卡通部分是由一个有界变差(BV)函数来刻画，相应的将BV罚项合并到变分泛函中需要解偏微分方程。
The cartoon component of an image is modeled by a bounded variation (BV) function; the corresponding incorporation of BV penalty terms in the variational functional leads to solve PDE equations.
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