复Monge—Ampere方程的特征值问题

讨论了复空间中强拟凸域上的复Ｍｏｎｇｅ－Ａｍｐｅｒｅ方程的特征值问题，证明了特征值问题解的存在唯一性，并给出了这个特征值与一类复空间中复Ｌａｐｌａｃｅ算子的第一特征值的关系，最后利用特征值及特征函数的存在性讨论了一类复Ｍｏｎｇｅ－Ａｍｐｅｒｅ方程的解的存在性及其分岐。     

COMPLEX MONGE-AMPEREEQUATIONS ON GENERAL DOMAINS

Abstract. The smooth solutions of the Dirichlet problems for the complex Monge-Ampere equa-tions on general smooth domains are found ,provided that there exists a C3 strictly plurisub har-monic subsolution with prescribed boundary value. It is the smooth version of an existence theo-rem given by Bedford and Taylor.     

椭圆型特征值问题正特征函数 的存在性和唯一性

本文讨论带Ｄｉｒｉｃｈｌｅｔ边值条件的非线性椭圆型特征值问题，给出了正特征函数存在和唯一的充分必要条件．     

一般区域上的抛物型Monge—Ampere方程（Ⅱ）

本文证明了一般光滑区域上抛物Ｍｏｎｇｅ－Ａｍｐｅｒｅ方程第一边问题古典解的存在性，推广了凸区域上相应的结果。     

Burgers－KdV 方程的初边值问题

该文借助适当的逼近，用散逸算子理论，差分和估计方法，证明了［０，１］×［０，Ｔ］上Ｂｕｒｇｅｒｓ－ＫｄＶ方程ｕｔ＋ｕ（ｘｘｘ）－Ｕ（ｘｘ）＋ｕｕｘ＝ｆ（ｘ，ｔ）的一类初边值问题存在唯一的解ｕ∈Ｌ∞（０，Ｔ；Ｈ３（０，１））∩Ｃ（０，Ｔ；Ｈ２（０，１））∩Ｗ（１，∞），（Ｏ，Ｔ；Ｌ２（０，１））．     

含参数拟线性薛定谔方程的特征值问题

本文考虑如下拟线性薛定谔方程:-Δu+(κu)/2△u²=λ|u|^p-2u,x∈Ω,这里u∈H(Ω),20,N≥3且Ω是有界区域.结合变分方法和摄动讨论,作者证明了存在常数κ₀> 0,使得对任何的κ∈(0,κ₀),这类特征值问题有解(λ,u).特别地,如果限制|u|_p^p=α,作者发现对任何的κ> 0,存在α₀> 0,使得在α <α₀时,该特征值问题的解总是存在的.此外,作者采用不同于Morse迭代的方法构造出了常数κ₀和α₀的精确表达式.     

BOUNDARY ELEMENT APPROXIMATION OF STEKLOV EIGENVALUE PROBLEM FOR HELMHOLTZ EQUATION

1.IntroductionWeconsiderthefollowingStekloveigenvalueproblem:FindnonzerouandnumberA,suchthat--An u=0,infi,on,on=An,onr,(1.1)wherefiCRZisaboundeddomainwithsufficientsmoothboundaryr,4istheonoutwardllormalderivativeonr.CourantandHilb..tll]studiedthefollowingeigenvalueproblem:onac=0,infi,--~An,onr,(1.2)OnwhichwasreducedtotheeigenvalueproblemofanintegralequationbyusingtheGreen'sfunctionofAn=0withNuemannboundarycondition.FromFredholmtheorem,weknowthat(1)theproblem(1.2)hasinfinitenumberofeigenv…     

CONVERGENCE AND SUPERCONVERGENCE OF HERMITE BICUBIC ELEMENT FOR EIGENVALUE PROBLEM OF THE BIHARMONIC EQUATION

Eigenvalue problem for biharmonic equation is an interesting and important problem, seeCiarlet and Lions[3]. In 1979, Rannacher[8] used the Adini nonconforming finite element tosolve this problem and obtained:Recedely, Yang[6] has proved that the order of covergence of Ah is just 2. The aim of this paperis to improve the order of convergence by using Hermite bicubic element. To our knowledge,there is not any result for approximation to the eigenvalue problem by using this element inliteratu…     

DERIVATIVES OF EIGENPAIRS OF SYMMETRIC QUADRATIC EIGENVALUE PROBLEM

Derivatives of eigenvalues and eigenvectors with respect to parameters in symmetric quadratic eigenvalue problem are studied. The first and second order derivatives of eigenpairs are given. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the quadratic eigenvalue problem, and the use of state space representation is avoided, hence the cost of computation is greatly reduced. The efficiency of the presented method is demonstrated by considering a spring-mass-damper system.     

ON THE LEAST SQUARES PROBLEM OF A MATRIX EQUATION

1.IntroductionThepurposeofthispaperistostudytheleastsquaresproblemofthematrixequationF~PGwithrespecttoPcSa,i.e.(PI)R\qIIF--PGll,whereF,GERnxmandG/0.Where11'11denotestheFrobeniusnorm,andSa~{XeS"fX20},S"={XER"""IX=X"}.Problem(PI)wasfirstformulatedbyAll...     

一类辛正交阵逆特征值问题及其最佳逼近

本文提出了一类辛正交阵的逆特征值问题,讨论了该问题有解的充分必要条件,给出了解的表达式,并考虑了解集合对给定矩阵的最佳逼近问题.     

非齐次对称特征值问题

引言 用SR~(n×n)表示所有。n×n实对称矩阵的集合。R~n表示n维线性空间。||·||_2表示向量的Euclid范数或矩阵的谱范数。 本文研究如下问题: 问题ISEP 给定矩阵A∈SR~n×n和向量b∈R~n,求实数λ和向量X∈R~n使得 AX=λX+b, (1) ||X||_2=1. (2) 若b=0,则问题ISEP就是通常的实对称矩阵特征值问题,若b≠0,则问题ISEP称为非齐次对称特征值问题,使(1)和(2)式成立的数λ和向量X分别称为非齐次特征值和相应的非齐     

一类二次特征值反问题的中心对称解及其最佳逼近

1引言给定n阶实矩阵M,C和K,二次特征值问题:求数λ和非零向量x使得Q(λ)x=0, (1．1)其中Q(λ)=λ2M λC K称为二次束．数λ和相应的非零向量x分别称为二次束Q(λ)的特征值和特征向量．Tisseur和Meerbergen概述了二次特征值问题的各种应用、数学理论和数值方法．在工程技术,特别是结构动力模型修正技术领域经常遇到与二次特征值问题相反的问题(称之为二次特征值反问题)．对阻尼结构进行动力分析时,应用有限元方法可得到系统的质量矩阵M,阻尼矩阵C和刚度矩阵K,从而可求得二次特征值问题的特征值(频率)和特征向量(振型)．但是有限元模型毕竟是实际结构系统的离散化,并且     

THE BI-SELF-CONJUGATE AND NONNEGATIVE DEFINITE SOLUTIONS TO THE INVERSE EIGENVALUE PROBLEM OF QUATERNION MATRICES

The main aim of this paper is to discuss the following two problems:λm)∈Hm×m, find A ∈ BSH≥n×n such that AX= X∧, where BSH≥n×n denotes the set of all n × n quaternion matrices which are bi-self-conjugate and nonnegative definite.Problem Ⅱ:Given B ∈ Hn×m, find -B∈SE such that ||B- B||Q = minA∈sE ||B - A||Q,necessary and sufficient conditions for SE being nonempty are obtained. The general form of elements in SE and the expression of the unique solution B of problem Ⅱ are given.     

A STABILITY ANALYSIS OF THE （k） JACOBI MATRIX INVERSE EIGENVALUE PROBLEM

In this paper we will analyze the perturbation quality for a new algorithm of the (k) Jacobi matrix inverse eigenvalue problem.     

THE EIGENVALUE PROBLEM EQUIVALENT TO MULTIVARIATE POLYNOMIAL SYSTEM

In this paper, the authors proved that finding all solutions of a given multivariate polynomial system is equivalent to solving a relative joint eigenvalue problem(Theorem 1) and in some cases one can find all solutions of the given system from the eigenvalues and vectors of one matrix or matrix pencil (Theorem 2). Especially the situation that the ideal generated by the given system is 0-dimensional is discussed.