ON HERMITIAN POSITIVE DEFINITE SOLUTION OF NONLINEAR MATRIX EQUATION X＋A^＊X^-2A=Q

Based on the fixed-point theory, we study the existence and the uniqueness of the maximal Hermitian positive definite solution of the nonlinear matrix equation X＋A^＊X^-2A=Q, where Q is a square Hermitian positive definite matrix and A＊ is the conjugate transpose of the matrix A. We also demonstrate some essential properties and analyze the sensitivity of this solution. In addition, we derive computable error bounds about the approximations to the maximal Hermitian positive definite solution of the nonlinear matrix equation X＋A^＊X^-2A=Q. At last, we further generalize these results to the nonlinear matrix equation X＋A^＊X^-nA=Q, where n≥2 is a given positive integer.     

ON SOLUTIONS OF MATRIX EQUATION AXAT ＋ BYBT=C

By making use of the quotient singular value decomposition (QSVD) of a matrix pair,this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the general solutions of the linear matrix equation AXA^T BYB^T=C with the unknown X and Y, which may be both symmetric, skew-symmetric, nonnegativede finite, positive definite or some cross combinations respectively. Also, the solutions of some optimal problems are derived.     

On The Maximal-Like Solution of Matrix Equation X ＋A^＊X^-2A=I^＊

In this paper,we study several iterative methods for finding the maximal-like solution of the matrix equation X A~*X~(-2)A=I,and deduce some properties of the maximal-like solution with these methods.     

EXISTENCE OF POSITIVE SOLUTION FOR A BIHARMONIC EQUATION

In this paper we consider the biharmonic equation (?) in a smooth bounded domain Ω (?) RN with boundary condition (?) where N ≥5, 1 < q < 2, λ>0 and 2= (2N)/(N-4). We prove the existence of λ such that for 0 < λ < λ the above problem has a positive solution.     

ON THE EXISTENCE OF POSITIVE ENTIRE SOLUTIONS FOR SINGULAR p-LAPLACE EQUATIONS

In this paper N-dimensional singular, p-Laplace equations of the following form are considered, where p ≥N, β > 0, and f : [0,∞)×(0,∞)×[0, ∞)→[0,∞) is a continuous function. Some sufficient conditions are obtained for the existence of infinitely many radially positive entire solutions of the equation which are asymptotic to positive constant multiples of |x|(p-N)/(p-1) for p > N or log|x| for N = p as |x|→∞.     

EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN SINGULAR BOUNDARY VALUE PROBLEMS OF FUNCTIONAL DIFFERENTIAL EQUATION

In this paper, the boundary value problems of p-Laplacian functional differential equation are studied. By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.     

POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER DELAY DIFFERENTIAL EQUATION

In this paper,we discuss the existence of positive solutions of the second- order delay boundary value problems.By applying the fixed-point theorem in a cone,we show the existence of at least one positive solution with singularity and the superlinear semipositone.As an application,we also give some examples to demonstrate our results.     

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO CERTAIN QUASILINEAR ELLIPTIC EQUATIONS IN A BALL

By the fixed point theorem on a cone and monotone iterative technique, the existence and multiplicity of the positive radial solutions to a class of quasilinear elliptic equations are considered. Also, using the monotone iteration method the authors deal with the boundary value problem as the nonlinear term f(t,u) increases in u.     

EXISTENCE OF POSITIVE SOLUTIONS AND 1／c-GLOBAL ATTRACTIVITY OF A NONLINEAR DELAY DIFFERENCE EQUATION WITH VARIABLE COEFFICIENTS

Abstract. The existence of positive solutions and the global attractivity of the difference equa-tion     

NONEXISTENCE OF POSITIVE SOLUTION OF A CLASS OF NONLINEAR DIFFERENCE EQUATION

In this paper, a class of nonlinear difference equations are investigated. The sufficient conditions for the nonexistence of positive solutions are obtained. The results in this paper improve ones in [2].     

矩阵方程X+A~*X~(-q)A=I(q>0)的Hermite正定解

1.引言 本文研究矩阵方程 X+A*X-qA=I (1)的Hermite正定解,其中I是一个n×n阶单位矩阵, A是一个n×n阶复矩阵, q是实数且q>0.q=1,q=2时的方程是从动态规划,随机过滤,控制理论和统计学中推导出来的,最近已有许多人对此进行了研究(见参考文献[1,2,4]),本文我们将研究方程(1)的解的存在性和解的性质,并讨论迭代求解及迭代解的收敛性. 对于Hermite矩阵X和Y,文中X≥Y表示X-Y是半正定的,X>y表示X-Y是正定的;对于方阵M,M*表示M的共轭转置,ρ(M)表示M的谱半径,λi(M)     

矩阵方程X+A^{*}X^{-q}A=Q(q\geq 1)的Hermitian正定解

本文研究矩阵方程X A~*X~(-q)A=Q(q≥1)的Hermitian正定解,给出了存在正定解的充分条件和必要条件,构造了求解的迭代方法.最后还用数值例子验证了迭代方法的可行性和有效性.     

矩阵方程X-A*XqA=I(0＜q＜1)Hermite正定解的扰动分析

首先证明了非线性矩阵方程X-A~*X~qA=I(0相似文献   

矩阵方程X-A~*X~qA=Q(q>0)的Hermite正定解

本文讨论了矩阵方程X-A*XqA=Q(q>0)的Hermite正定解,给出了q>1时解存在的必要条件,存在区间,以及迭代求解的方法．证明了0相似文献   

矩阵方程X-A~*X~(-1)A=Q的Hermite正定解及其扰动分析冰

考虑非线性矩阵方程X-A~*X~(-1)A=Q,其中A是n阶复矩阵,Q是n阶Hermite正定解,A~*是矩阵A的共轭转置.本文证明了此方程存在唯一的正定解,并推导出此正定解的扰动边界和条件数的显式表达式.以上结果用数值例子加以说明.     

矩阵方程X+A*X-nA=I的正定解

In this paper we give some sufficient conditions and some necessary conditions under which the matrix equation X A^*X^-nA=I has a positive definite solution. An iterative method which converges to a positive definite solution of this equation is constructed. And an error estimate formula on this iterative method is also derived.     

矩阵方程A^TXB=C的正定和半正定解

给出了矩阵方程Ａ＾ＴＸＢ＝Ｃ在正定和半正定矩阵类中有解的充要条件及解的一般表达式。     

矩阵方程AXA^T＋BYB^T=C的对称正定解

本研究矩阵方程AXA^T BYB^T=C的对称正定解。利用广义奇异值分解（GSVD）给出了该矩阵方程有解的充分条件及解的通式。     

关于矩阵方程X+A*X-nA＝I的正定解

本文对任意正整数n界定了矩阵方程X A*X-nA=I的正定解的特征值的范围,给出了它的极大正定解一个充分条件.