查询词典 existence theorem

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

Based on the segmented unstructured model of Nosiheptide fermentation process, the secondary variables are selected according to the implicit function existence theorem. The on-line identification of fermentation phases is accomplished by using an indicator variable which is gained by mathematical inference, and for each phase, a local soft sensor model is developed.

首先以分阶段的诺西肽发酵过程非结构模型为基础，根据隐函数存在定理进行辅助变量的合理选择；然后利用经数学推导得到的指示变量"伪比生长率"完成发酵阶段的在线辨识，并采用神经网络构建出对应于各阶段的局部软测量模型。

According to the estimation of biomass in Nosiheptide fermentation process, the secondary variables are selected according to the implicit function existence theorem, and then a soft sensor model of biomass is developed by using the IBPNN. The testing result shows the effectiveness of the presented approach.

最后针对诺西肽发酵过程中菌体浓度的估计问题，根据隐函数定理选取辅助变量，应用IBPNN建立菌体浓度软测量模型，实验结果验证了所提方法的有效性。

In chapter 4, we first discussed the existence of multiple positive solutions of the second order nonsingular Dirichlet boundary value problem for impulsive differential equations by using the fixed point index theorem in cones . Next, we presented some new existence results for singular boundary value problems for second order impulsive differential equations by using fixed point theorem in cones and Leray-Schauder nonlinear alternative theorem.

第四章我们首先利用锥不动点定理讨论了非奇异二阶脉冲微分方程狄利克莱边值问题多个正解的存在性；其次我们用锥不动点定理和Leray-Schauder型非线性抉择定理，讨论了奇异二阶脉冲微分方程狄利克莱边值问题一个及多个正解的存在性。

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。

Under the suitable hypotheses of compactness,convexity,and semicontinuity,an existence theorem of the weak efficient solution for the convex-like vector equilibrium problems is established.

向量变分不等式与向量均衡问题的重要课题之一是研究其解集的连通性，因为它保证了解可连续的移动。

In this paper,we introduce the concepts of efficient solution for vector variational inequalities and f-quasimonotone operator,and give an existence theorem for vector variational inequalities in Banach spases.

引进了向量变分不等式有效解以及f－拟单调算子的概念，并给出了Banach空间中拟单调向量变分不等式的有效解的存在性定理

By regarding the forest-sum growth-cutting rate as the control variable and judging its optimality by "norm minimum", we have given a existence theorem of the optimal control for the area distributing systems of forest trees by utilizing space L2(0,T)'s reflexivity, smoothness and strict convexity.

本文将林木总和长消率作为控制变量，以"范数最小"来衡量其最优性，利用空间L2（0，T），T＞0的自反、光滑和严格凸性，给出了森林面积分布系统最优控制的一个存在性定理。

Shen prove a short time existence theorem for manifolds with umbilical boundary. He also derived the Simons' identity for the boundary under the Ricci flow. And as a corollary, Shen show that any three-manifolds with totally geodesic boundary which admits positive Ricci curvature can be deformed to a space form with totally geodesic

而带边流形上的Ricci流的研究始于Shen，在1996年，Shen在中考虑带边三维流形上的黎曼度量的Ricci形变，证明了如果初始三维流形的黎曼度量具有正Ricci曲率和全测地边界，则此三维黎曼流形上存在着常正曲率的黎曼度量。

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。

Do not gum up the work by telling mother what we are going to do .

别告诉母亲我们要干的事，那会把事情搞糟的。

In recent years, application of the partial prestressed concrete beam s is developed.

近年来，随着部分预应力砼梁应用的推广，发现我国规范所采用的名义拉应力法的计算结果不稳定。