运用不动点定理，研究一类具状态依赖时滞的微分方程周期正解的存在性。
By applying a fixed point theorem, the authors study the existence of positive periodic solutions to a class of differential equations with stated-dependent delay.
针对对称导数、对称偏导数，给出了一些新形式的微分中值定理。
In this paper, symmetric derivative and symmetric partial derivative are researched and some new differential mean value theorems are defined.
我们利用边界层校正法以及微分不等式理论证明了解的存在定理，并构造出其解的一致有效渐近展开式。
Using the method of boundary layer correction and the differential inequality theory, we prove the existence theorem of solutions and construct the uniformly valid asymptotic expansions of.
本文建立了具有阻尼项的高阶微分方程新的振动定理。
This paper obtains a new oscillation theorem of high-order differential equation with damping.
讨论了一般微分单项式的导数的值分布，提出一个新的定理，并进行较为详细的证明。
The paper discusses the value distributions of the derivative of differential monomials, presents a new theorem and proves it in more details.
给出了某类六阶非对称微分算子在一些合适拓扑下关于复参数的几个线性同构定理。
This paper provides several linear isomorphism theorems for certain nonsymmetric differential operators of sixth order under proper topologies about some complex parameters.
本文利用定积分的性质、微分中值定理、施瓦兹不等式、二重积分等内容，研究了积分不等式的四种证法。
This article explores the four ways for solving integral inequality with the nature of definite integral, mean value theorem of differentials, Schwarz inequality and double integral.
给出系统的时间积分等式，并由此等式导出类能量方程、类维里定理、一个积分变分原理和一个微分变分原理。
A power-like equation, a Virial-like theorem, an integral variational principle and a differential variational principle for the system are deduced by using the time-integral identity.
讨论了一类二阶强次线性时滞微分方程解的振动性质，建立了三个新的振动性定理。推广和改进了已知的一些结果。
The oscillation of a class of second order strongly sublinear delay differential equations is discussed. Three new theorems are established. The results generalize and improve some known ones.
术文研究泛函数微分方程数值解的混合算法，给出了收敛性定理及数值例子。
In this pager hybrid methods of functional differential equations are investigated. Some convergence theorems are given and numerical example are presented.
讨论了一类二阶强次线性时滞微分方程解的振动性质，建立了三个新的振动性定理。
The oscillation of a class of second order strongly sublinear delay differential equations is discussed. Three new theorems are established.
对于受速率为常数约束的运动质点，可以应用动能定理建立其运动微分方程。
The differential equations of motion of a particle constrained to moving in a constant speed are deduced from the kinetic energy theorem.
给出了微分中值定理的一个推广形式，并将所得结果应用于凸函数性质的研究。
This article gives a spreading form of the mean value theorem of differential and applies the gained results to the quality of convex function.
构造辅助函数是利用微分中值定理解决问题的关键，构造辅助函数的方法较多。
Constructing auxiliary functions is the key in using differential mean value theorem to solve problems; there are many methods for constructing auxiliary functions.
本文将实分析中的微分中值定理推广到复分析中，得到了相应的结果。
In this paper, the differential mean value theorem of real analysis is extended to the complex analysis and correspondence results are obtained.
以分割区域d为基础将解析函数与共轭解析函数的微分中值定理推广到高阶形式。
Basing on a partition of region d, we generalize the differential mean-value theorems for analytic functions and conjugate analytic functions to a high order case.
接着，仿微分几何的曲线论，建立了基本公式和唯一存在定理。
Then the basic formulae and the theorem on its unique existence have been established as doing in the curve theory in Differential Geometry.
其中关于均方全微分和均方方向导数的定理是多指标随机过程所特有的结论。
Four of them, i. e. the theorems on the mean-square total differential and mean-square directional derivative are special conclusions of the multiple parameter stochastic processes.
本文就恰当微分方程的积分因子问题进行推广，得出两个定理。
This article makes an extension on the problem of integral factor in the total differential equation and has drawn two theorems.
从热力学第二定理出发，利用外微分构造了熵、焓以及吉布斯函数的表达式。
Expressions of entropy, enthalpy and Gibbs function are formulated by exterior differential derived from second law of thermodynamics.
常微分方程中经典的存在性定理不能使用。
Often the existence axioms of classic in the differential calculus square distance can't use.
在证明中采用了一种把网微分法与条件矩母函数相结合应用于随机选择系统强极限定理研究的一种途径。
In the proof, the tools of the conditional moment generating function and the differentiation on a net for the study on strong limit theorems in the random selection system are applied.
得到一个关于脉冲微分方程弱指数渐近稳定的判定定理。
The sufficient conditions of the weak exponential asymptotic stability of impulsive differential system are obtained.
摘要通过对积分算子谱的估计，作者给出了一阶线性微分差分方程在边值条件下解的存在唯一性定理。
In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition.
微分中值定理是微分学的基本定理。
Differential medial value theorem is the basic theorem of the calculus.
给出了拉格朗日微分中值定理和第一积分中值定理中值点的渐进性的更一般性的结果及其简洁证明。
Gives more general results on the gradualness of the median point of Lagranges median theorem and first median theorem for integrals and its succinct proof.
根据引力场的两个定理，导出了引力势的微分和积分形式。
Consequent differential form and integral form of gravitational potential are deduced from the two laws of gravitational field.
在微分几何定理证明中，一个定理成立的辅助条件(非退化条件)不是惟一的，但越简单越好。
The subsidiary conditions (or called non-degeneracy conditions) are not one and only that a theorem holds in differential geometry theorem proving.
本文指出了有关微分中值定理“中间点”的渐近性四篇文章的结果中的错误，并给予修正。
This paper points out and revises some errors in the results found in four articles concerning the asymptotic behavior of the "Intermediate points" of the mean value theorem.
本文指出了有关微分中值定理“中间点”的渐近性四篇文章的结果中的错误，并给予修正。
This paper points out and revises some errors in the results found in four articles concerning the asymptotic behavior of the "Intermediate points" of the mean value theorem.
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