查询词典 existence theorem of implicit function

The existence of solutions for two-point boundary value problem subject to nonlinear second order differential equation with mixed boundary conditions is studied by using topological transversality theorem, and some known results are improved.

现利用拓扑横截定理，考虑了二阶常微分方程两点边值问题在组合边界条件下的解的存在性，对二阶常微分方程两点边值问题所对应的辅助问题作先验界估计，并利用拓扑横截定理，得到了边值问题解的存在性，推广了一些已有结果。

This paper was concerned with the Dirichlet-Neumann mixed boundary value problem of bipolar quantum hydrodynamic model in thermal equilibrium. By truncation method and Leray-Schauder fixed point theorem, the existence of solution to the problem is proved. In addition, the uniqueness of the solution was proved as the Plank constant was large enough.

研究了热平衡状态下双极量子流体动力学模型的Dirichlet-Neumann混合边值问题，利用截断方法和Leray-Schauder不动点定理证明了其解的存在性，另外还证明了当普朗克常数充分大时其解是唯一的。

Using the asymptotically compact theory of Anselone' and Stepleman' theorem, the existence, the unicity , the convergence and the error estimate with O(h3) of the discrete equations are shown....

并借助Anselone的渐近紧收敛理论和Stepleman定理，证明了离散方程组的解存在性、唯一性、收敛性和精度阶O(h~3)。使用Ostrowski的不动点定理，提供了三阶收敛的迭代法。

At first, using fixed point theorem, we establish the sufficient conditions which guarantee the existence, uniqueness, uniform stability of periodic solutions for the equations.

首先，我们利用不动点定理，建立了保证该类方程周期解的存在性、唯一性及一致稳定性的充分条件。

The existence of pointwise robust convergent algorithm and uniformly robust convergence is next investigated. We propose an optimal l〓 robustness synthesis method for structured perturbations system by taking advantage of the famous Small Gain Theorem.

证明了最优l〓辨识算法的存在性；证明了黑箱辨识存在辨识算法使全局误差收敛于有界区间；提出并证明了逐点鲁棒收敛算法的存在性；证明了一致鲁棒收敛算法的存在性。

An existence and uniqueness theorem of local solvability is proven for this equation, and compared with the existing results, the author's conditio ns restri cted to the nonlinear term of this equation are much general.

文章所给出的结果的适用性要远大于已有的与此问题相关的结论，对此方程非线性项的假设要比一般的多。

For instance, we obtained the existence and uniqueness theorem and several judgement theorems on stability and instability for several types of nonlinear singular systems. Using Z-transformation, we estabilished the response formula of discrete singular systems with delay, and obtained the sufficient and necessary condition of rearchability.

如我们得到了某些非线性广义系统解的存在唯一性定理，及稳定与渐近稳定的判据；利用Z变换方法，得到了滞后离散广义系统的一般响应公式，进而得到了局部可达与局部能控的充要条件等。

For diffusive Predator-Prey model with Holling-Ⅲ functional response without time delay, shooting argument together with LaSalle's Invariance Principle and the Hopf bifurcation theorem are applied to prove the existence of traveling wave solutions and small amplitude traveling wave train solutions.

在数学理论的研究中，行波解可以揭示方程本身的许多重要性质；在实际应用中，行波解可以很好的表现自然世界中的振荡现象。因此，对反应扩散方程行波解的研究具有非常重要的意义。

Due to the moving base existence of the minehunting and the frame structure characteristic of the sonar array, a new modeling thought in which the boat body coordinates is regarded as moving coordinates and the whirligig equation of sonar array compared with the self coordinates is founded on the basis of the Euler's theorem and the coordinate transform is introduced.

由于猎雷艇作为动基座的存在和声纳基阵的框架结构特点，提出了以艇体坐标系为运动坐标系，运用变形的欧拉定理和坐标变换建立声纳基阵相对自身坐标系的旋转运动方程的建模思想；将所建立的矢量形式的动力学模型展开整理，获得了状态矩阵形式的猎雷声纳基阵动力学方程，为系统动力学模型的实用化奠定了基础。

Due to the moving base existence of the minehunting and the frame structure characteristic of the sonar array,a new modeling thought in which the boat body coordinates is regarded as moving coordinates and the whirligig equation of sonar array compared with the self coordinates is founded on the basis of the Eulers theorem and the coordinate transform is introduced. The dynamic equations of minehunting sonar array with the state matrix form are founded by settling the dynamic models with the vector form. So it offers theory foundation for analyzing the dynamic characteristic and designing robust control.

由于猎雷艇作为动基座的存在和声纳基阵的框架结构特点，提出了以艇体坐标系为运动坐标系，运用变形的欧拉定理和坐标变换建立声纳基阵相对自身坐标系的旋转运动方程的建模思想；将所建立的矢量形式的动力学模型展开整理，获得了状态矩阵形式的猎雷声纳基阵动力学方程，为系统动力学模型的实用化奠定了基础。

"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。