查询词典 monotone decreasing function

Aimed at the mathematic problem in the model of the pendulum oscillation,the paper introduces the study on the existence of odd-harmonic solutions to second order semi-linear differential equation which describes the model of the pendulum oscillation by using upper and lower solution method monotone iterative technique and the Schauder fixed point theorem respectively.

针对摆型振动模型中的数学问题，分别采用上下解方法、单调迭代法及Schauder不动点定理研究了摆型振动模型的二阶半线性微分方程奇调和解的存在性。

The dynamics of coupled system of semilinear parabolic equations with time delays is investigated using upper and lower solutions and its associated monotone iterations. The asymptotic behavior of solutions is given.

利用上、下解方法及相应的单调迭代序列研究具有时滞的耦合半线性抛物方程组的动力学行为，给出了解的渐近性质。

In this paper, we will prove the existence and uniqueness of solutions for singular boundary value problems of differential equations by using the mixed monotone method.

本文利用混合单调迭代法来证明几种奇异微分方程边值问题解的存在唯一性。

In chapter 3, as one of the main parts of this thesis, by using the mixed monotone method, we discussed the existence and uniqueness of singular elliptic boundary value problems.

第三章我们将用混合单调迭代法来证明奇异椭圆微分方程边值问题解的存在唯一性。

Our conclusion is : For general transport equation and some special transport equations (slab geometry, spherical symmetry, pillar symmetry) we can evaluate some relevant physical quantities and geometrical properties from the exiting photon flux. The method we will use is to transform the transport equation into integral equation by integrating it along its characteristics, then we prove the nonlinear operator K is monotone and continuous with respect to its arguments and obtain the existence of K~-1. Consequently, we can evaluate some relevant physical quantities and geometrical property of the medium.

我们得到的结论是：无论对于一般的迁移方程，还是当介质具有某种对称性时(板对称、球对称、柱对称)的迁移方程，我们都可以根据泄漏的光子流估计介质各种相关物理量和几何特性，所用方法都是将迁移方程通过沿特征线积分转化为积分方程的形式，然后证明非线性算子K关于自变量的单调性和连续性，从而得到逆算子K~(-1)存在，进而达到估计介质各种相关物理量和几何特性的目的。

VIRAG:(His mouth projected in hard wrinkles, eyes stonily forlornly closed, psalms in outlandish monotone) That the cows with their those distended udders that they have been the the known...

692维拉格：（嘴上吸出深深的皱纹，两眼像石头般绝望地紧闭着，以异国情调。用单音咏诵圣歌。）那些乳房胀鼓鼓的母牛，它们四远驰名

We divide the existence of generalized solutions into three theorems becauseof the existence of a generalized supersolution we need in the proof.To ob-tain this fact,we discuss three different cases separately.WhenΩhas strictconvexity,it can be proved that the generalized supersolution of (1)(2)is theconvex-monotone hull of 〓in 〓,this is theorem 2.WhenΩdoesn't hasthe strict convexity,in theorem 3 we have to suppose there exists a generalizedsupersolution.

我们的广义解的存在性结果之所以分成三个定理陈述，主要是因为在我们的存在性证明中，一个重要的事实就是广义上解的存在性，而为了得到这个事实，我们分别讨论了三种不同的情况：在定理2中的假设〓具有严格凸性时，我们证明了问题（1）（2）的广义上解就是初边值〓的凸单调包，而在〓没有严格凸性时，我们在定理3中假定了一个广义上解的存在性。

Our methods are based on the the surjection of maximal monotone operators and the critical point theorem of convex functionals.

本文主要利用极大单调算子满射原理和凸泛函临界点理论对半线性抛物型方程在各种控制下的能控性进行了研究。

Based on the surjection of maximal monotone operators, we prove that some semilinear heat equations with weak Lipschitz nonlinear terms are exactly controllable by L〓 0, T: H〓(Ω control; Based on the critical point theorem of coercive convex functionals, we prove that some parabolic equations with Lipschitz nonlinear terms are globally approximately controllable and finite-dimensional exactly controllable by controls acting on mobile supports, and finally, we extend the results to parabolic equations in R〓.

首先利用极大单调算子的满射原理证明了半线性热方程在较弱Lipschitz条件下可通过L〓0.T；H〓(Ω控制实现精确能控。然后通过构造强制凸泛函并利用其临界点理论证明了带Lipschitz非线性项的抛物型方程可通过作用在在移动支集上的控制来实现整体近似能控与有限维精确能控，最后将整体近似能控与有限维精确能控结论推广到无界区域R〓上。

Among the windings of the violins And the ariettes Of cracked cornets Inside my brain a dull tom-tom begins Absurdly hammering a prelude of its own, Capricious monotone That is at least one definite "false note.——Let us take the air, in a tobacco trance, Admire the monuments, Discuss the late events, Correct our watches by the public clocks. Then sit for half an hour and drink our bocks.

随着小提琴的抑扬及铜号嘶哑的小咏叹调我的脑中响起了沉闷的咚咚声荒谬的敲打它自己的前奏曲，任意无常的单调那根本是一个明显的"错音"——让我们换一换空气，在烟熏的恍惚间，敬仰那些纪念碑，讨论时下新闻，跟街钟对表，然后坐上半个小时，喝点烈性的黑啤酒。

Cable dampener cannot be rolled up but must be hung over the cable.

缆帆不能被卷起，必须保证处于展开状态

"This skylark is a present from my master," he says.

"这只云雀是我主人献上的礼物。"他说。