充分条件

For the comparison equations, the sufficient conditions for the existence of nonoscillatory solutions are also given by using fixed point theorem.

对于比较方程，也用不动点定理给出了非振动解的存在的充分条件。

By using the fixed point index theorem, several sufficient conditions for the existence of at least one or infinte positive solutions are obtained.

利用不动点指数定理研究了一类二阶非线性常微分方程的三点边值问题正解的存在性问题，得到了至少存在一个或无穷多个正解的几个充分条件。

Some sufficient conditions for the existence and multiplicity solutions of positive periodic solutions were obtained by using the fixed point theorem .

讨论一类具分布时滞的微分方程正周期解问题，利用锥不动点定理，获得了这类问题正解存在性和多重性的充分条件，推广和改进了已有文献的相关结果。

Some sufficient conditions for the forced oscillation of solutions of the systems are obtained.

研究具有连续分布滞量的非线性中立型双曲偏泛函微分方程系统，获得了该类系统解强迫振动的充分条件。

In this paper, the oscillation of forced neutral difference equations with positive and negative coefficients is studied and two sufficient conditions of this equation to be oscillatory are obtained.

研究了一类具有强迫项正负系数中立型差分方程的振动性，获得了方程振动的两个充分条件。

The sufficient conditions for achieving synchronization of this fractional differential system are derived by using the stability criterion of fractional linear equation.

用三种不同的方法考虑分数阶Lorenz混沌系统的修正投影同步，基于分数阶线性方程的稳定性理论给出了实现同步的几个充分条件，数值模拟说明了所给方法的有效性。

Using the method of approximating the Lipschitz functions by the convex functions, we give a sufficient condition for the set where Lipschitz functions on a Hilbert space are Frechet differentiable is a residual set.

我们利用Lipschitz函数空间中凸函数的逼近性质来分析Lipschitz函数的微分性质，得到Hilbert空间上Lipschitz函数的Frechet可微点集是剩余集的一个充分条件，以标题"Lipschitz函数与凸函数之间的一些联系"在中国科学杂志上发表。

In chapter 4, sufficient conditions of at least one, two and multiple positive periodic solutions to a scalar functional differential equation with muti-finite delays are obtained by using a fixed point theorem introduced in [27] and [85] which is different from the one of a cone compression and expansion of norm type. It generalizes and improves some related results in the literature.

第四章利用文献[27]和[85]中所给出的不同于范数型锥压缩和拉伸的不动(来源：bc1cbcABC论文网www.abclunwen.com)点定理得到了具有有限时滞纯量泛函微分方程至少存在一个、两个和多个正周期解的充分条件，推广并改进了已有的相关结果。

Using the theory on delay functional and impulsive differential equation, sufficient condition with time delay for the permanence of the system was obtained. And it was proved, that time delays, pulse vaccination and vertical transmission can bring obvious effects on the dynamics behaviors of the model.

运用脉冲时滞泛函微分方程理论，获得了含有时滞的持久性的充分条件，并且证明了时滞、脉冲免疫与垂直传染对模型的动力学行为能够产生显著的影响。

Based on Lyapunov functional theory and linear matrix inequality, the suffcient condition of delay-dependent guaranteed cost control law with time-varing is derived and the minimal cost supper is given.

基于Lyapunov函数的理论，并运用线性矩阵不等式导出了该系统时滞依赖的保性能控制律存在的充分条件以及最小性能上界。

She gently rebuff ed him, but agreed that they could be friends

她婉言拒绝了，但同意作为朋友相处。

If in the penal farm, you were sure to be criticized.

要是在劳改农场，你等着挨绳子吧！