本文研究当极限方程有奇性时四阶线性常微分方程的柯西问题解的渐近式。
This paper studies the asymptotic expression of solution of Cauchy's problem for a forth order equation when the limit equation has singularity.
本文主要运用锥不动点定理和格林函数研究二阶非线性常微分方程组正解的存在性。
In this paper, we study the existence of positive solutions to second - order nonlinear ordinary differential equations by using fixed point theorem in cones and Green's function.
用首次积分法，讨论了带奇异边界条件的非线性常微分方程解的存在性、不存在性和唯一性。
By the first integral method, the existence, uniqueness and nonexistence of solutions for some nonlinear ordinary differential equations with singular boundary condition are discussed.
受控系统的运动设为变系数线性常微分方程组所描述，而系统的终点状态是相空间内的某一凸性区域。
We assume that the motion of controlled object is describedby linear ordinary differential equations with variable coefficient, and the final states ofthe system form a convex region of phase space.
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.
文中得到几个振动性准则和离散谱准则，并将这些结果应用到常微分方程。
Some oscillatory criteria and discrete spectrum criteria are given, and we can apply them to the ordinary differential equations.
标准奇异点是微分代数方程系统区别于常微分方程系统的一个标志性的拓扑结构，具有重要的理论研究意义。
The standard singular point is an important structure of the differential-algebraic equation systems(DAEs), by which DAEs are differentiated from the ordinary different equation systems (ODEs).
应用常微分方程定性方法，得到了正平衡点的全局稳定性和非小振幅极限环的存在唯一性的充分条件。
By using the qualitative methods of ODE, the positive equilibrium's global stability and existence and uniqueness of non-small amplitude stable limit cycle were obtained.
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.
利用MATLAB进行一阶常微分方程的计算机辅助教学，探讨用MATLAB进行一阶常微分方程辅助教学的可行性、方便性。
The CAI teaching of a first-order ordinary differential equation is discussed with computer MATLAB software, and its feasibility and convenience is introduced.
研究一类非线性四阶常微分方程两点边值问题，得到一个存在唯一性定理。
The uniqueness and existence theorem for a nonlinear fourth-order boundary value problem is established.
把所得结果应用于研究常微分方程积分边值问题正解的存在性，所得结果推广和本质上改进了马如云等作者最近的一些结果。
Finally the main results are used to establish some existence results for positive solutions of integral boundary value problems for ordinary differential equations.
该文讨论由经典-脉冲混合控制最优策略中提出的一类常微分方程的自由边值问题，给出了该问题解的存在性定理。
This paper discusses a class of free boundary value problem of ordinary differential equations occurred in problems of classical mixed and impulse optimum control in research fund management problems.
利用该正交性，得到无限个仅阻尼项耦合的关于时间的常微分方程及相应的初始条件。
Using the orthogonality of characteristic functions, a series of ordinary differential equations and their initial conditions are derived.
考虑具有介质阻尼及非线性粘弹性本构关系的梁方程，证明了它的有界吸收集和有限维惯性流形的存在性，并由此得到在一定的条件下所给偏微分方程等价于一常微分方程组的初值问题。
The equations of nonlinear viscouselastic beam are considered, The existence of absorbing set and inertial manifolds for the system are obtained, and from which we get that the P D E.
考虑具有介质阻尼及非线性粘弹性本构关系的梁方程，证明了它的有界吸收集和有限维惯性流形的存在性，并由此得到在一定的条件下所给偏微分方程等价于一常微分方程组的初值问题。
The equations of nonlinear viscouselastic beam are considered, The existence of absorbing set and inertial manifolds for the system are obtained, and from which we get that the P D E.
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