查询词典 existence theorem of implicit function

The second section: Under the conditions of nonlinear boundary controbility, we consider the initial boundary value problem of Camassa—Holm equations with dissipative. By using the contractive mapping fixed point theorem and a priori estimates, the existence of global smooth solution, global attractor in H〓, time periodic solution or almost-periodic solution and the global exponential stability are proved.

第二部分：在非线性控制边界条件之下，对于带耗散项的Camassa—Holm方程的初边值问题，用压缩映射不动点原理及先验估计方法，证明了整体光滑解的存在性、整体解的指数稳定性、H〓空间中整体吸引子的存在性以及时间周期解和殆时间周期解的存在性。

In the chapter 3,we base on the existence of periodic solution ,using the method of linearization and applying the mean value theorem and the variation-of-constants formula, we get the sufficient condition of the exponential stability of periodic solution of a class of nonlinear functional differential system .

在第三章中，建立在系统周期解存在的基础上，利用线性化的方法，根据微分中值定理和常量变差公式，得到了一类非线性泛函微分系统周期解指数稳定的充分条件。

A complete novel assumption is presented. Then, we prove the existence of two nontrivial solutions for a class of second order superlinear difference systems with the help of Minimax principle and Linking theorem in critical point theory,.6. Two applications in physics are given. Firstly, a coupled differential system coming from second harmonic waves is discussed.

利用Ricceri建立的三临界点定理，证明了一类含参数二阶差分方程在某些新的条件下至少存在三个解；随后，利用临界点理论中的极小极大原理和环绕定理，讨论了一类二阶超线性差分方程组多重解的存在性。

By use of the stretch and compression fixed point theorem of normic form in cone ,the sufficient conditions for the existence of monotone increasing positive solutions and monotone decreasing negative solutions are obtained to the boundary value problems.

运用锥拉伸与锥压缩不动点定理，分别得到了边值问题单调递增正解和单调递减负解存在的充分条件。

By using saddle point reduction and Morse theory,we obtain an existence theorem of three periodic solutions for this equation.By means of E~+-Morse theory established by A.

本章还首次应用临界点理论研究中立型泛函微分方程的次调和解，在变分泛函中允许含有时滞变量，从而给出了研究这类方程周期解的新途径。

In this paper, using Moser Twist Theorem, we obtain the existence of quasi-periodic solutions and the boundedness of solutions for Duffing equations and Liénard equation with some symmetric structure.

本文将利用Moser的扭转定理来研究Duffing方程和具有某种对称性的Liénard方程的拟周期解的存在性以及解的有界性。

In the last 20 years, many mathematicians used Moser Twist Theorem to study more complicated dynamics for nonlinear oscillations, such as the existence of quasi-periodic solutions and invariant tori, the Lagrange stability, etc.

近20年来，国内和国际上的一些数学家开始利用Moser的扭转定理来研究非线性振动的更为复杂的行为，如拟周期解和不变环面的存在性，解的Lagrange稳定性。

In this paper the existence of fixed point problems for nonlinear operator is studied; several new fixed-point theorem are established and some related known work is extended and improved.

本文研究了几类非线性算子不动点的存在性问题，建立了若干新的不动点定理，推广了前人的一些结果。

By using the continuation theorem of topology degree theory and properties of nonsingular M-matrix, we obtain sufficient conditions for the existence of positive periodic solutions of this system.

利用拓扑度理论中的连续定理以及M-矩阵的性质获得了该系统正周期解存在的充分条件。

The existence and uniqueness of solution for population dynamics and the corresponding maximum principle are obtained by using Banach's fixed point theorem and the concept of normal cone.

第二节和第三节分别对具有年龄结构的竞争两种群和n种群扩散系统的最优收获问题进行了研究，获得了相应的极大值原理，以及两种群竞争系统最优控制问题解的存在唯一性。

"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。