奇摄动四阶椭圆型偏微分方程

本文用微分不等式理论讨论了一类奇摄动四阶椭圆型偏微分方程,得到了在整个区域上一致有效的渐近展开式.     

奇摄动向量椭圆型积分微分方程边值问题

本文利用上、下解方法首先研究了一类向量椭积分微分方程问题的存在性，并应用所得结果，借助伸缩坐标法研究一类相应的奇摄动问题的边界层现象的解的一致有效渐近展开式。     

无界区域上的奇摄动半线性椭圆型方程

本文研究了一类无界区域上的半线性椭圆型方程的边值问题。在一定的条件下,利用微分不等式方法证明了存在一个解并得到在整个区域上为一致有效的解的渐近展开式。     

非局部半线性椭圆型方程奇摄动问题

今考虑如下奇摄动非局部半线性椭圆型方程边值问题：ε为正的小参数，x＝（x1，x2，…，xn）∈Ω，Ω为n维欧氏空间的有界域，Ω为Ω的光滑边界，L＝为Ω上的一致椭圆型算子，为外法向导数．假设：（H1）L的系数及f,g，Ki关于其变元在相应区域内为充分光滑的函数；（H2）fy（x,     

高阶半线性椭圆型方程奇摄动边值问题

本文研究了一类高阶半线性椭圆型方程奇摄动边值问题,利用比较定理,证明了渐近解的一致有效性。     

一类具有非局部边界条件的半线性椭圆型方程奇摄动问题

本文研究了一类具有非局部边界条件的奇摄动半线性椭圆型方程边值问题。在适当的条件下，利用比较定理讨论了问题解的渐近性态。     

高阶拟线性椭圆型方程奇摄动问题

本文利用微分不等式和多重尺度，研究了一个高阶椭圆型偏微分方程摄动边值问题，并得到了一致有效的渐近展开式。     

拟线性椭圆型方程奇摄动边值问题

本文讨论了拟线性椭圆型方程奇摄动Robin边值问题。在适当的条件下，利用不动点定理，研究了边值问题解的存在唯一性及其渐近性态。     

奇摄动半线性时滞微分方程边值问题

本研究半线性时滞微分方程边值问题εx″(t)=f(t,x(t),x(t-ε）,ε）,t∈（0,1),x(t)=ψ（t,ε）,t∈[-ε,0],x（1)=A(ε）。利用不动点原理及微分不等式理论,我们证明了边值问题的存在性,并给出了解的一致有效渐近展开式。     

THE SINGULAR PERTURBATION OF NONLOCAL BOUNDARY VALUE PROBLEMS FOR NONLINEAR ELLIPTIC EQUATION OF FOURTH ORDER

A class of singularly perturbed nonlocal problems for nonlinear elliptic equation of fourth order are considered. The uniformly valid asymptotic expansion of the solutionis obtained.     

THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER SEMILINEAR ELLIPTIC EQUATIONS

Considerasingularlyperturbedproblemforhigherorderselnilinearequationswhereeisasmallpositiveparameter,ndenotesaboundedregioninRe,whereonsignifiesasmoothboundaryofn,misaintegerandjk,gi,k,j=0,'',in--1,aresufficientlysmoothfunctionswithregardtotheirvariablesincorrespondenceranges.Modealwiththesingularperturbationforthesecondorder'ellipticequations[1],[2],thefourthorderequations[3]l[4]andaclassofhigherorderequations[5].Inthispaperttheauthorsconsiderthesingularperturbationforevenmoregeneralhigheror…     

一类高阶半线性椭圆型方程奇摄动广义边值问题

讨论了半线性椭圆型方程奇摄动广义边值问题.在适当的条件下研究了对应的边值问题广义解的存在唯一性及其渐近性态.     

SINGULAR PERTURBATION OF OPTIMAL CONTROL FOR SEMILINEAR INTEGRO-DIFFERENTIAL EQUATIONS

1 IlltroductionWe shall solve a problem Of optimal control consisting of the systemon the interval 0 5 t 5 1, with initial conditionsand the quadratic cost functionalwhich is to be minimized. Here the "T" denotes transposition; I = jot K(t, asx) fi are m-vectors; is gi are n-vectors, u is an r--vector, and the matrix R.is symmetric and positive definite, while the matrices Q and T are symmetricand positive semidefinite throughout 0 5 t S 1 for E > 0 small. fi, g2, 51 and6z are matrix functi…     

MODIFIED MORLEY ELEMENT METHOD FOR A FOURTH ORDER ELLIPTIC SINGULAR PERTURBATION PROBLEM

This paper proposes a modified Morley element method for a fourth order ellipticsingular perturbation problem. The method also uses Morley element or rectangle Morleyelement, but linear or bilinear approximation of finite element functions is used in the lowerpart of the bilinear form. It is shown that the modified method converges uniformly in theperturbation parameter.     

NON C~0 NONCONFORMING ELEMENTS FOR ELLIPTIC FOURTH ORDER SINGULAR PERTURBATION PROBLEM

In this paper we give a convergence theorem for non C^0 nonconforming finite element to solve the elliptic fourth order singular perturbation problem. Two such kind of elements, a nine parameter triangular element and a twelve parameter rectangular element both with double set parameters, are presented. The convergence and numerical results of the two elements are given.     

一类高阶椭圆型方程Dirichlet问题

本文讨论了一类奇摄动高阶椭圆型方程Dirichlet问题，利用伸长变量和变界层校正法，得到了问题解的形式渐近展开式．再用微分不等式理论，证明了解的一致有效性．     

UNIFORMLY CONVERGENT NONCONFORMING ELEMENT FOR 3-D FOURTH ORDER ELLIPTIC SINGULAR PERTURBATION PROBLEM

In this paper, using a bubble function, we construct a cuboid element to solve the fourth order elliptic singular perturbation problem in three dimensions. We prove that the nonconforming CO-cuboid element converges in the energy norm uniformly with respect to the perturbation parameter.