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Finaly, in the case of the nonlinearities being singular at 0, by utilizing the mountain-pass theorem and some other variational methods, we get the existence of nontrivial solutions of the equations under the Dirichlet boundary condition, where the operator diva(x,u is the p-Laplacian.

最后，我们通过应用山路引理等变分方法，研究当算子diva(x，▽u为p-Laplacian并且非线性项在原点有奇异性时，方程在Dirichlet边值条件下非平凡解的存在性。

R~n(n≥0) is a bounded domain with smooth boundaryΩ;ΔisLaplace operator; u and v, respectively, denote populaton densities of prey andpredator species, inhabit the domainΩ; a_i, b_i, c_i, D_i(i=1,2) are positive constants.the form of boundary parameter B is?

R~n(n≥0)是边界Ω充分光滑的有界区域；△为Laplace算子；u，v分别表示区域Ω中食饵和捕食者的密度，参数a_i，b_i，c_i，D_i(i=1，2)均为正常数，而边值参数B形式为这里的？

Firstly, we get the necessary and sufficient conditions for Toeplitz operators that commutes with another such operator whose symbol is a monomial, meanwhile, we completely characterize when the mellin transform of the bounded function on the interval 0,1 is a rational function.

首先得到了以有界函数为符号的Toeplitz算子和以单项式函数为符号的Toeplitz算子可交换的充要条件，同时给出了0，1区间上的有界函数的Mellin变换为有理函数的充要条件。

In the second chapter, we prove that if a bounded operator S satisfies some integrab...

第二章证明了在单位圆盘D上的加权Bergman空间A~p

Finally we show that the discrete fra-ctional integral operator〓is bounded on〓.

本章还证明了离散分数次积分算子〓在〓上的有界性。

In this dissertation, we mainly discuss the resonance theorems for families of linear and nonlinear operators, and the theory of bounded linear operator space in F~* spaces.

本文主要研究F~*空间上的线性、非线性算子族的共鸣定理和有界线性算子空间理论。

We show that in error estimates,the condition number 〓 of any invertiblelinear bounded operator T in Banach spaces is minimal.

第III部分考虑条件数在Banach空间中扰动分析的极小性质。

A novel neural network model, named delayed standard neural network model, is proposed, which is the interconnection of a linear dynamic system and a bounded static delayed nonlinear operator.

摘要提出一种新的神经网络模型---时滞标准神经网络模型，它由线性动力学系统和有界静态时滞非线性算子连接而成。

Based on the delta operator bounded real lemma, sufficient condition with an H〓 norm bound on closed loop uncertain systems and state feedback design are provided.

基于Delta算子的界实引理，给出了闭环不确定系统具有H〓范数界的充分条件及状态反馈设计方法。

Besides,we investigate the compatibility of the pair,where A is a bounded linear self-adjoint operator on a complex Hilbert space H and S is a closed subspace of H.

此外，对由一个自伴算子A和一个闭子空间S组成的元素对的兼容性进行了研究。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。