查询词典 existence theorem of implicit function

From this theorem, we prove the existence of the recurrence for the admissible q-proper hypergeometric sums, and obtain an estimate of the order J of the recurrence.

在此基础上证明admissible q-proper超几何和的迭代关系的存在性，并且得到迭代关系阶数J的一个估计。

By using the Krasnoselskii fixed point theorem, an existence result of two positive solutions is obtained under suplinear condition and sublinear condition.

讨论一类四阶非线性微分方程组Dirichlet边值问题正解的存在性，利用Krasnoselskii不动点定理得到这类边值问题在超线性和次线性条件下至少存在两个正解。

This generalizes a theorem ofFan on the existence of long cycles in unweighted graphs to weighted graphs.

这个结果推广了Fan关于在非赋权图中最长圈的一个重要定理。

This thesis mainly investigates the single food chain Chemostat models, analyzing the stability of equilibrium points, the existence and uniqueness of periodic solutions as well as the Hopf bifurcation theorem.

本文主要探讨单食物链微生物培养模型的解的稳定性，周期解的存在性和唯一性以及分支问题。

The following exciting results are revealed: 1 When considering the influence of some nonlinear elements such as hard-limit of exciters, the effects of some devices such as Power System Stabilizer and Static Var Compensator which can introduce positive damping in power system, the reasonability of system parameter values in simulation, the SNB surface and HB surface on the boundary of SSSR will turn close to each other and even coalesce together; 2 Under some conditions, coupling between slow exciters and shunt capacitors will bring negative damping in power system dynamics, which increases the possibility of oscillatory instability. So the power system with mass shunt compensators is easily subjected to the oscillatory instability. In recent years, chaotic phenomena of power system have been reported many times. Some simulation studies even found chaos existing inside the power system SSSR. In this dissertation, chaotic phenomena in power systems are thoroughly studied in order to make clear the relation of chaos and SSSR. The following results are derived: 1 Based on Li-Yorke Theorem and their definition on the chaos, the existence of chaos in power system is verified; 2 Three possible routes of causing chaos in power system are found and deeply investigated. They are route of cascading period doubling, route of directly initial energizing and route of torus bifurcation (or quasi-periodicity). The latter two routes are investigated for the first time in power system stability studies; 3 When the stability conditions of chaos are broken, it is found they can lead to voltage collapse, angle divergence, or voltage collapse with angle divergence simultaneously.

针对在电力系统小扰动稳定区域内可能存在混沌吸引域的有关报道，本文深入研究了电力系统混沌现象的出现途径和与系统失稳模式之间的关系：1利用Li-Yorke定理和Li-Yorke的混沌定义，从理论上证明了电力系统混沌现象的存在性；2发现了电力系统中导致混沌出现的三种可能途径：倍周期分岔导致混沌、初始能量直接激发混沌和经由环面分岔导致混沌，并对后两种新发现的途径进行了较为细致的研究；3发现了混沌极限环破裂导致电压崩溃、角度失稳以及电压崩溃和角度失稳同时出现的现象，其中混沌极限环破裂导致系统角度失稳和电压崩溃及角度失稳同时出现的现象均属首次报道；4证明由微分-代数方程描述的系统模型，其小扰动稳定域的边界只包含HB、SNB和SIB三种分岔界面，在SSSR的内部和边界上，均不可能存在会导致混沌的点，从而将混沌现象排除在小扰动稳定域的研究之外，简化了后者的研究工作。

The existence and convergence theorem of Newton method and quasi Newton method solving nonlinear equation with parameters F = 0 is obtained under point estimates and weak conditions.

在点估计条件下给出用Newton法及拟Newton法求解带参数非线性方程F = 0解的存在性定理和收敛性定理，以及误差估计。

Using this theorem, we proved the existence of traveling wave solutions in cooperative Lotka-Voterra system with stage structure.

本文用这个存在性定理证明了带时滞分年龄段的Lotka-Volterra模型的两个平衡点之间行波解的存在性。

Firstly in§2.1, by applying the fixed point theorem the existence of positive solutions for second-order three-point boundary value problem is discussed.

第二节，运用不动点定理研究四阶两点边值问题正解的存在性。

In Chapter 2, an existence theorem is obtained for periodic solutions of non-autonomous second order systems with even-typed potentials. We also investigate solutions of linear bounded positive self-conjugation operators equations in Hilbert Space by variation methods.

第二章主要利用临界点理论中的归药方法、极小作用原理研究具偶型位势的二阶非自治系统周期边值问题，得到了周期解的存在；利用变分方法证明了Hilbert空间中有界线性正自共轭算子方程解的存在性。

By Ricceri's three critical points theorem, the existence of solutions for a class of quasilinear elliptic systems with variational structure was proved and the location of the solutions was also determined.

通过运用Ricceri的一个三临界点定理，讨论了一类具变分结构的拟线性椭圆方程组，获得了多解的存在性，并且给出了解的位置。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。