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The model in this paper takes the form as belowThe main contents and results in this paper are as follows:In section 1, we state our main analytical results on equilibria of the above system. First, several sufficient conditions for coexistence of the steady-state are given by the standard fixed-point index theory in cone. Second, the global structure of the coexistence solutions and their local stability are established by using bifurcation theory. Third, the multiplicity, uniqueness and stability of positive steady-state solutions to this system are derived by means of perturbation theory of eigenvalues, standard regularity theory, Sobolev embedding theorem and fixed-point index theory.

本文主要有两章内容：第一章研究了该模型正平衡解的性质，可分为三部分：第一部分运用极值原理、上下解方法和锥映射不动点指标理论得到正平衡解存在的充分条件；第二部分利用分歧理论给出了平衡态系统正分歧解的结构，并讨论了局部分歧解的稳定性；第三部分利用特征值扰动理论、标准椭圆正则化理论、Sobolev嵌入定理及指标理论讨论了正平衡解的多重性、唯一性及稳定性，并讨论了参数对解的影响。

According to the studied results at present, the studied objects are mainly thin plate and beam about sound radiation mode, a method computed sound radiation mode of complex structure is presented in this dissertation, according to the results of the previous two chapter, a theoretical method to solve acoustical radiation mode and acoustical radiation efficiency of complex structure by boundary element method and acoustical radiation theory is posed, the acoustical radiation power is expressed as a Hermitian quadratic form, while the radiation modes is determined by general eigenvalue decomposing, and then the radiation efficiency is computed via the orthodoxy of radiation modes with regard to impedance matrix and average velocity matrix; lastly, the validity of the method is proved by pulsating sphere and radiating cube with analytical results. According to results of the form three chapter, the structure sound radiation sensitivity is studied in detail, the sound radiation power of structure can be expressed as positive Hermitian quadratic form, the sound radiation sensitivity can be expressed as two parts by partial differential with respect to design variable, which are sensitivity of boundary velocity and impedance matrix, combined with the theory of FEM and BEM, the structure sound radiation can be translated to the analysis of structure dynamic sensitivity and impedance matrix sensitivity. The theory posted in this dissertation is tested by the FEM software ANSYS and the software AAS programmed by author.

在前几章的基础上，通过结构声辐射的模态理论对结构的声辐射的机理进行了深入地探讨，针对目前声辐射模态的研究对象主要是简单的板和梁类结构，提出了一种计算复杂结构声辐射模态的方法，利用前两章研究所得的结论，将边界元方法与广义特征值的理论结合起来研究了复杂结构的声辐射模态与声辐射效率，先将结构的声辐射功率表示为一个正定的厄米特二(来源：ABb7C论文0909网www.abclunwen.com)次型，运用广义特征值分解求解了复杂结构的声辐射模态，然后利用声辐射模态关于阻抗矩阵与均方速度耦合矩阵的正交性，求解了复杂结构的声辐射效率，最后用具有解析解的脉动球与辐射立方体验证了该方法的有效性。

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。

The whole contents is divided into five chapters. In chapter 1, as the beginning of this paper, we offered some relative knowledge, such as the cone theory and semi-order method in nonlinear functional analysis. Moreover, we established a new fixed point theorem of the mixed monotone iterative operator.

全文共分成五章：第一章作为准备知识给出了本文要用到的相关知识内容，其中包括非线性泛函分析中的锥理论及半序方法，并建立了新的混合单调算子不动点定理。

In chapter 2, by virtue of the properties of partially ordered F-type topological space, we establish some fixed point theorems of increasing mappings in this kind of space. At the same time, we investigate the existence of maximum fixed point and minimum fixed point of increasing mappings on an order interval.

第二章，利用半序F-型拓扑空间的基本性质，建立这类空间上单调增映射的不动点定理，研究其序区间上单调增映射的最大、最小不动点的存在性。

The third chapter introduces the basic concepts and notations of geometric singular perturbation theory.

第三章简要地介绍了奇异摄动的基本概念，方法，特别是几何奇异摄动理论。

This chapter clarifies the nested relationship between the matrix family of unitary, orthogonal, Givens, Householder, permutation, and row or column symmetric matrices. A precise correspondence of the singular values and singular vectors between the unitary-symmetric matrix and its mother matrix is derived and proved (hence a fast algorithm of singular value decomposition for unitary-symmetric matrix is straightforwardly obtained), and the corresponding perturbation bound is provided.

该章揭示了酉对称矩阵、正交对称矩阵、 Givens 对称矩阵、 Householder 对称矩阵、置换对称矩阵和行对称矩阵之间的逐级包含关系；推导并证明了，酉对称矩阵的奇异值和奇异向量与母矩阵的奇异值和奇异向量之间的定量关系，据此可得酉对称矩阵奇异值分解的快速算法；给出并证明了摄动矩阵的摄动界。

The deformation compatible equation based on the catenary cable element is derived in chapter 2, and corresponding program is made to solve the accurate distribution of the prestress for cable dome. During the solving, two-nodes bar elements and catenary elements are adopted for the struts and cables of structure respectively. As the cable dome is a kinematically indeterminate system, its solving process is also derived in detail and the equations, which are based on large distortion, are adopted to solve the problem.

第二章推导了基于悬链线解析解的索单元变形协调方程式，并编制了相应计算程序对索穹顶结构精确的预应力分布进行求解，结构分析时压杆采用两节点直线杆单元，索采用悬链线索单元；考虑到索穹顶结构属于动不定结构体系，文中还对动不定体系的求解过程进行了详细的推导，同时采用建立在大变形基础上的变形协调方程来求解结构体系的有限机构位移。

In Chapter 2, the introduction of the dynamical models is presented, furthermore, on the basis of analyzing perturbation factors there are two dynamical models fit for the motion situation of the NEAs, which are imported as the restricted authentic particle model and the restricted mean particle model (with respect to the treatment of the orbits of the perturbing major planets) that the Post-Newtonian effect is also taken into account, while for the latter the influence of the 5/2 (or 2/5) resonant items of the interaction between the Jupiter and the Saturn is considered.

第二章是关于力学模型的介绍，在分析摄动因素的基础上，引入了近地小行星运动中比较合适两种力学模型，即限制性质点真实模型与限制性质点平均模型(这一平均指的是对摄动源大行星轨道的处理)，在两种模型中均考虑了后牛顿效应，另外在平均模型中还考虑了木星与土星之间的5/2(2/5)共振项的影响。

Finite element method and nonlinear regression method is used to discuss the relationship of Y shape steel tube joint's local translational displacement and local translational stiffness to the ratio between the width and the thickness of main tube, ratio of width and thickness between branch tube and main tube and included angle between branch tube and main tube's the axial directions.

本章分析了Y形方管节点的平动位移和平动刚度随主管宽厚比、支主管宽度比、支主管厚度比和支主管轴线夹角等参数的变化关系，并从各回归方程及回归系数的显著性检验可知回归方程的准确性。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。