本文从非线性微分方程的解过渡到线性稳定分析，从而讨论出稳定态与非稳定态的情况。
In This paper, linear steady analysis is Made from the solution of non-linear differential equation and Luther, the situation of steady state or non-steady state is discussed.
本文应用可积的一类线性微分方程求出了非均质变截面弹性直杆振动问题的一个精确解，我们应用这一精确解验证了渐近解的精确度。
This paper gives an exact solution for free vibration of a physically nonuniform straight bar with varying section by the use of a class of integrable linear ordinary differential equation.
利用不动点理论，给出了一类半线性微分方程有界的调和伪概周期解存在的充分条件。
Using fixed point theorems, in this paper we give sufficient conditions of the existence of bounded mild pseudo almost periodic solution for some semilinear differential equations.
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.
给出了带有双侧共振的非线性微分方程周期解存在性的一个新的结果。
A new result about existence of periodic solutions of nonlinear differential equations with double resonance will be given.
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.
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.
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.
由于非饱和流动的数学模型归结为非线性的偏微分方程，除了一些很特殊的情况外，很难得到解析解。
It is very difficult to get analytic solution except some very specific cases for the model owing to nonlinear partial differential equation.
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.
一般说来，线性微分方程属于解起来最简单的一种。
Linear differential equations are, generally speaking, among the simplest to solve.
利用时滞脉冲积分不等式，给出了一类非线性的脉冲时滞微分方程的解有界性的充分条件。
Sufficient conditions for boundedness of solutions of nonlinear delay differential equations with impulses are established by using impulsive integral inequalities with a deviation.
为了研究混沌运动，对一类非线性动力系统的自由振动方程进行了求解，继之给出了单层扁锥面网壳非线性自由振动微分方程的准确解。
In order to study chaos movement, Accurate solution of non-linear free vibration differential equation is by solving a kind of free vibration equation of non-linear dynamics system.
本文利用微分方程单位解矩阵估计的相关方法，得到了确定含有非线性电阻的动态电路唯一稳态的条件。
Based on the estimation of the unit solution matrixes of differential equations, the unique steady state of the dynamic circuits with nonlinear resistors is studied by matrix measure.
讨论了一类二阶强次线性微分方程解的振动性质，获得了三个新的振动性定理，推广和改进了相关文献的结果。
The oscillation for solutions of the class of the second order strongly sublinear differential equation are discussed and three new oscillation theorems are obtained.
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.
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.
最后给出了一些数值例子，证实了这个分数阶线性多步法是解分数阶常微分方程的一个有效方法。
Finally, some numerical examples are provided to show that the fractional order linear multiple step method for solving the fractional order ordinary differential equation is an effective method.
本文列出了一维点阵非谐振动的非线性微分方程组，并求出了这组方程在相应边值条件下的解析解。
The exact solutions of a set of non-linear differential equations with limiting conditions describing the anharmonic vibration of a one-dimensional lattice have been obtained.
本文研究了一类一阶变系数非线性滞后型微分方程解的振动性，得到这类方程仅有振动解的充分条件。
The study is made on the oscillation of a class of the first order nonlinear retarded differential equations with variable coefficients, and the sufficient conditions are obtained.
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.
在一定的条件下我们证明了非线性互补问题的解是该微分方程系统的平衡点，并且证明了该微分方程系统的稳定性和全局收敛性。
We prove that the solution of a nonlinear complementarity problem is exactly the equilibrium point of differential equation system, and prove the asymptotical stability and global convergence.
文中给出了这一非线性振动模型的微分方程，并用奇异摄动法求得了渐近解。
This paper also gives the differential equation of the nonlinear vibration model, and obtains its asymptotic solution by means of singular perturbation methods.
研究了三阶非线性脉冲时滞微分方程解的振动性与渐近性，得到了一些充分判据。
The oscillation and asymptotic behaviors of three order nonlinear functional differential equation with impulses are investigated, and some sufficient conditions 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.
研究了几类K阶整系数线性微分方程解的超级、零点收敛指数和零点超收敛指数，得到一些精确的结果。
The hyper order, the exponent of convergence and the hyper-exponent of convergence of zeros of solutions for some types of K-order linear differential equations with entire coefficients are discussed.
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.
应用谐波平衡法对系统三阶非线性微分方程组解析分析，与数值解比较验证了解析解的正确性和有效性。
The method of harmonic balance is applied to study the non-linear dynamic response of the third-order nonlinear partial differentiation system.
应用谐波平衡法对系统三阶非线性微分方程组解析分析，与数值解比较验证了解析解的正确性和有效性。
The method of harmonic balance is applied to study the non-linear dynamic response of the third-order nonlinear partial differentiation system.
应用推荐