本文试应用求解一阶线性微分方程的方法导出几类常见的函数项级数的求和公式。
The sum formulas of several kinds of ordinary series with function term are deduced by using the method of solving linear differential equation.
根据一阶拟线性偏微分方程组的特征理论，讨论内弹道两相流方程组的类型。
Following the theory on characteristics of first order quasi-linear partial differential equations, classification of the balance equations for two-phase flow in interior ballistics is discussed.
采用了压缩性的坐标变换后，推导得到了五个一阶导数的微分方程组。
Using a compressibility coordinate transformation, a set of the first derivative differential equations has been derived.
可分离变量的一阶微分方程是一类特殊的一阶微分方程，它在实际中有着广泛的用途。
Separable variables are a special class of first order differential equations, which has a wide range of USES in practice.
对峙反应动力学过程，其实质是一个求解一阶常微分方程的过程。
Essentially, the opposite reaction kinetics process is a process of resolving the first order ordinary differential equation.
研究了一类具有混合边界条件的奇摄动二阶积分微分方程边值问题。
This paper studies a class of singularly perturbed two order integral differential equation boundary value problem with mixed boundary conditions.
对二阶变系数非线性微分方程的常系数化给出两个使其可积的条件，并举例论证。
The two conditions of the second order nonlinear differential equation with variable coefficient are given and expounded with examples.
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.
本文研究了两类具体含逐段常变量微分方程的伪概周期解的存在性问题和一类一阶微分方程组的数值解。
In this paper, the existences of almost periodic solutions and pseudo almost periodic solutions for several classes of functional differential equations are investigated.
在第二部分中，同样的方法，我们讨论了一阶脉冲微分方程积分边值问题。
In part II, by the same way, we consider first-order impulsive differential equations with integral boundary value problems.
目的研究一阶具有分段常数变量的脉冲微分方程的解的性质。
Objective to investigate characters of the solution to first order impulsive differential equations with piecewise constant arguments.
研究具时滞的三阶非线性微分方程，利用变量替换和不动点方法，得到了此方程有界解和概周期解的存在性及唯一性结果。
This paper deals with the problems on the existence and uniqueness of bounded solutions and almost periodic solution for third order nonlinear differential equations with time lag.
利用锥上的混合单调算子不动点定理，本文研究了一类四阶奇异非线性微分方程的边值问题，即一类弹性梁方程问题。
By using a fixed point theorem of mixed monotone operators in cone, this paper studied a fourth-order nonlinear singular boundary value problem, namely a class of elastic beam equation.
有关算符的统计平均值随时间的演化满足一个封闭的一阶线性微分方程组。
The statistical average values of some relevant operators satisfy a set of differential equations of the first order.
本文利用物理学中常见的热传导理论，形象地阐释了二阶齐次线性偏微分方程的本质。
With the ordinary theory of Heat Exchange in physics this essay visualizes the essence of second-order homogenous linear partial differential equations.
结论的普遍性可以推广到数学力学学科，并给出了这一类三阶非线性微分方程求定性解的一般方法。
The universality of the conclusion can be spread to mathematics and mechanics science also and give a popular method to solving this third-order nonlinear differential equation qualitatively.
经典的数理方程大量的是二阶线性偏微分方程。
Classical mathematical equations is the large number of second-order linear partial differential equations.
本文给出了数值求解一类偏积分微分方程的二阶全离散差分格式。
In this paper, the second order fully discrete difference method for a partial integro-differential equation is considered.
本文讨论了一交通模型的一阶拟线性偏微分方程激波产生唯一性的条件并给了严格的证明。
A condition of a one-order quasilinear partial differential equation of a traffic model forming unique shock wave is given end proved.
本文研究了既有滞后量又有超前量的一阶中立型常系数微分方程的振动性，得到了其振动的几个充分条件。
In this paper, we have studied the oscillation of the first order neutral functional differential equations with delay and advanced argument, obtained, some sufficient conditions extended and impoved.
本文旨在研究求解非凸约束优化问题的基于二阶导数的微分方程方法。
The aim of the dissertation is to study second order derivatives based differential equation approaches to nonconvex constrained optimization problems.
第三章讨论了奇数阶微分方程解的振动性，建立了一系列解振动的充分条件。
Chapter three mainly considers linearized oscillation for odd-order neutral differential equations, and some sufficient conditions will be established.
针对该微分方程的非线性特点，采用一阶谐波平衡法，进行了动力响应的计算分析。
The harmonic balance method(HBM)was employed to solve the forced response of damped blades considering nonlinear feature of differential equations.
本文首先给出了一类具有无穷多个周期解的无阻尼二阶线性偏微分方程所描述的系统。
This paper is devoted to study the existence of an infinitude of periodic solutions for a class of second order linear PDE systems without damping.
本文研究了二阶变系数线性常微分方程的一种近似求解方法。
In this paper, we study an approximate solution of the second-order linear ordinary differential equations with variable coefficients.
这组算子的统计平均值随时间的演化满足一个封闭的一阶线性微分方程组。
And the evolution of the statistical average values of the set of operators with time satisfy a group of one-order linearly differential equations.
用孤立不变集和孤立块的概念，给出了含一个参数的二阶常微分方程组的非驻定有界解分支点的存在性准则。
Using concepts of invariable set and isolated cube, we obtained existence for bifurcate points of bounded solutions of second order ordinary differential systems including a parameter.
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.
应用类比法，给出了一类五阶非线性微分方程零解的全局渐近稳定的充分条件。
In this paper, analogy method is used to discuss the global, asymptotical and stable zero solution of non-linear five-order differential equation.
应用类比法，给出了一类五阶非线性微分方程零解的全局渐近稳定的充分条件。
In this paper, analogy method is used to discuss the global, asymptotical and stable zero solution of non-linear five-order differential equation.
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