作为应用，研究了一类起源于动态规划的泛函方程组公共解的存在性问题。
As applications, the existence of common solutions for a class of system of functional equations arising in dynamic programming are discussed.
泛函网络是类似于人工神经网络的新型网络模型，是泛函方程的网络表达形式。
Functional network is new network model. It is similar to artificial neural network and is network expression of functional equation.
从而获得了原不可解泛函方程的解析递推表达式和一个易于实施的控制律的解析解。
Thus, the explicit recursive expression of the original unsolvable functional equation and a control law with easy implementation are obtained.
从稳定电流场基本方程出发，通过定义线性微分算子，推导出与之等价的泛函方程。
According to the fundamental equation of steady current field, the corresponding functional equation is obtained by use of the linear differential operator.
本文讨论了动态规划中提出的一类更一般的泛函方程组公共解和重合解的存在性问题。
Some existence theorems of common and coincidence solutions for a class of more general systems of functional equations arising in dynamic programming are shown.
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.
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.
利用拓扑度理论对一类非线性泛函差分方程周期解的存在性进行了讨论，得到该问题周期解的一个存在定理。
The existence of periodic solution to nonlinear functional difference equation is considered by using the topological degree, and a periodic solution of this problem is obtained.
在广义标准材料理论框架下，利用本构泛函展开法，推导出弹性各向同性损伤演化方程的一般形式。
Thus, in the framework of generalized standard materials, the damage evolution equation for isotropic elastic damaged materials has been derived.
利用压缩映照定理，研究了一个二阶泛函差分方程边值问题，得到存在和唯一性定理。
By using the contraction mapping principle, the boundary value problems for a second order functional difference equation are investigated.
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.
随后，基于图像复原统一能量泛函的欧拉·拉格朗日方程，导出一种非线性数字滤波器的统一设计框架。
The unified designing framework for nonlinear digital filters is subsequently derived, through solving the Euler-Lagrange equation of the unified energy functional.
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.
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.
利用压缩映照定理，研究了一个二阶泛函差分方程边值问题，得到存在和唯一性定理。
By using the contraction mapping principle, the boundary value problems for a second order functional difference equation are investigated. Existence and uniqueness results are obtained.
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.
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.
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.
运用泛函分析和积分方程理论，证明了系统解的存在性与唯一性，得到系统解的解析表达式。
Applying the theory of integral equation and functional analysis, we prove the existence and uniqueness of the system solution to the equation, and get the analytical expression of the solution.
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.
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.
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.
再利用泛函的临界点理论，得到了方程具有周期解的充分条件。
Some sufficient conditions for the existence of periodic solutions of the equation are obtained by using the theory of critical point in functional.
基于矩形板的势能泛函导出其特征方程。
Characteristic equation of a rectangular plate is derived based on its potential energy functional.
本文研究一类高阶泛函偏微分方程边值问题的强迫振动性。
In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.
研究了间断非线性常微分方程奇摄动泛函边值问题。
The singularly perturbed functional boundary value problems for the discontinuous nonlinear ordinary di? Erential equations are considered.
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.
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.
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