正方程组正解的存在性

本文推广了文[1]的结果,给出了正方程组存在正解的某些新条件.

一类超线性奇异半正方程组正解的存在性

通过把所研究的问题转化为相应的全连续算子的不动点问题,利用范数形式的锥拉伸与锥压缩不动点定理得出了一类二阶超线性奇异半正方程组在m点边值条件下正解的存在性结果,并给出了一个例子作为对所获结果的应用.

一类四阶超线性奇异半正方程组正解的存在性

通过把所研究的问题转化为相应的全连续算子的不动点问题,利用范数形式的锥拉伸与锥压缩不动点定理得出了一类四阶超线性奇异半正方程组在两点边值条件下正解的存在性结果.

高阶奇异半正微分方程组多点边值问题的正解

应用范数形式的锥拉伸与锥压缩不动点定理得出了一类高阶超线性奇异半正方程组在点边值条件下正解的存在性结果。最后用实例验证了该结论的应用价值。

一类临界指数增长的椭圆型方程组正解的存在性

研究了一类临界指数增长的椭圆型方程组。通过变分法,得到方程组的能量泛函在零点附近的局部极小值点的存在性,且该极小值点为方程组的正解。证明了当方程组的扰动项趋于零时,方程组的正解也趋于零。

关于正线性方程组正解的判定定理

给出正线性方程组正解的概念,给出并证明了正线性方程组正解的若干判别方法,对教学有一定的指导意义.

正线性方程组正解判别的两个结果

非齐次线性方程组在科学计算和日常生活中会经常出现的,在研究实际问题中也会接触系数和右端项皆为正的方程组,而研究它有正解更有实际意义.对正线性方程组给出了合理的变形,对其正解的判别给出了若干方法,得到一些重要结果.

正线性方程组的半正解

通过引入正线性方程组Ax=b的可去变量,得到了没有可去变量的正线性方程组有无穷多个半正解情形的充分必要条件以及有惟一半正解情形的充分必要条件.

线性方程组的正解

讨论了线性方程组正解的若干性质,给出了线性方程组有正解的一个充要条件,以及由此得到的求正解的一般方法,还介绍了正解问题的若干应用.

新辅助方程法构造(2+1)维修正的色散水波方程组的新精确解

利用辅助方程法的构造性和机械化性特点,引入一种新的辅助方程,给出该方程的几种由双曲函数、三角函数和有理函数通过不同形式复合而成的精确解.以(2+1)维修正的色散水波方程组为例,借助符号计算系统Mathematica,在行波变换下获得了该方程的新的复合型精确解.

正线性方程组正解的判别

本文给出了正线性方程组正解的概念。

算子方程组的正解及在半正微分边值系统的应用

证明了半正算子方程组x=λK_1F_1(x,y),y=λK_2F_2(x,y)正解的存在性结果,其中λ>0为参数,P为实Banach空间E中一个完全锥,K_1,K_2:P→P为线性全连续算子,F_1,F2:P→E为连续有界算子.作为应用,给出了一类半正微分边值系统正解存在性的结果.

带有积分边界条件的非线性四阶奇异微分方程组的正解

通过构造一个特殊的锥,并在锥上应用不动点定理,得到了具有积分边界条件的四阶奇异微分方程组单个正解、多个正解的存在性和方程组正解的不存在性.

Existence of Positive Solutions for a Class of Degenerate and Nondegenerate Stable Diffusion Models

This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions.

Minor Self-conjugate and Skewpositive Semidefinite Solutions to a System of Matrix Equations over Skew Fields

Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.

Existence and Regularity of Solution to a Thermally Coupled Nonstationary System

In this paper, a coupled elliptic-parabolic system modeling a class of engineering problems with thermal effect is studied. Existence of a weak solution is first established through a result of Meyers＇ theorem and Schauder fixed point theorem, where the coupled functions σ（s）,k（s） are assumed to be bounded in the C（IR×（0, T））. If σ（s）,k（s） are Lipschitz continuous we prove that solution is unique under some restriction on integrability of solution. The regularity of the solution in dimension n ≤ 2 is then analyzed under the assumptions on σ（s） ∈w^1,∞（Ω×（0, T）） and the boundedness of σ＇（s） and σ″（s）.

An Orthogonal Approach to Reusable Component Discovery in Cloud Migration

As an innovative software application mode,Software as a service(SaaS) shows many attractive advantages.Migrating legacy system to SaaS can make outdated systems revived.In the process of migration,the existing valuable components need to be discovered and reused in order that the target system could be developed/integrated more efficiently.An innovative approach is proposed in this paper to extract the reusable components from legacy systems.Firstly,implementation models of legacy system are recovered through reverse engineering.Secondly,function models are derived by vertical clustering,and then logical components are discovered by horizontal clustering based on the function models.Finally,the reusable components with specific feature descriptions are extracted.Through experimental verification,the approach is considered to be efficient in reusable component discovery and to be helpful to migrating legacy system to SaaS.

The Smoothness of Weak Solutions to the System of Second Order Differential Equations with Non-negative Characteristics

In this paper,we will discuss smoothness of weak solutions for the system of second order differential equations eith non-negative characteristies.First of all,we establish boundary,and interior estimates and then we prove that solutions of regularization problem satisfy Lipschitz condition.

Symmetry and nonexistence of positive solutions to an integral system with weighted functions

Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(x) and K(x) satisfy some suitable conditions.It is shown that every positive regular solution(u(x)1,v(x)) is symmetric about some plane by developing the moving plane method in an integral form.Moreover,regularity of the solution is studied.Finally,the nonexistence of positive solutions to the system in the case 0 < p1q <(n+α)/(n-α) is also discussed.

Fracture analysis near the interface crack tip for mode Ⅰ of orthotropic bimaterial

The mechanical behaviors near the interface crack tip for mode Ⅰ of orthotropic bimaterial are researched. With the help of the complex function method and the undetermined coefficient method, non-oscillatory field if the singularity exponent is a real number, and oscillatory field if the singularity exponent is a complex number are discussed, respectively. For each case, the stress functions are constructed which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions, the system of non-homogeneous linear equations is obtained. According to the necessary and sufficient condition for the existence of solution for the system of non-homogeneous linear equations, the singularity exponent is determined under appropriate condition using bimaterial parameters. Both the theoretical formulae of stress intensity factors and analytic solutions of stress or displacement field near the interface crack tip are given. When the two orthotropic materials are the same, the classical results for orthotropic single material are deduced.