QUASI-DIAGONALIZATION FOR A SINGULARLY PERTURBED DIFFERENTIAL SYSTEM WITH TWO PARAMETERS

By two successive linear transformations,a singularly perturbed differential system with two parameters is quasi-diagonalized. The method of variation of constants and the principle of contraction map are used to prove the existence of the transformations.     

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases:ε/μ2→0(μ→0),μ2/ε→0 (ε→0) andε=μ2, the uniformly valid asymptotic solution is obtained by using the expansion method of two small parameters and the theory of differential inequality.     

在局部区域上的奇摄动非线性方程Robin边值问题

本文是讨论一类在局部区域上的奇摄动非线性Robin边值问题。利用算子理论和不动点原理，得到了相应问题解的存在性和唯一性。     

A KIND OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM FOR NONLINEAR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS

§ 1　IntroductionSince 1 970 the perturbed boundary value problems for functional differential equationshave been derived in many fields,such as biology,physics,optimal control and e-conomies[1 ] .Some works on studying it have appeared,for example references[2～ 6] .Inthis paper,we study a kind of singularly perturbed boundary value problems for Volterrafunctional differential equations:εx″(t) =f(t,x(t) ,[Tx] (t) ,x(t-τ) ,x′(t) ,ε) ,t∈ (0 ,1 ) ,(1 )x(t) =φ(t,ε) ,t∈ [-τ,0 ] ,ax(1 )…     

一类双参数奇摄动非线性反应扩散方程

本文研究了一类双参数非线性反应扩散奇摄动问题的模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的情形下作了讨论.得到了该问题的渐近解,由解的展开式看出本问题的解同时具有初始层和边界层.     

THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM OF NONLINEAR INTEGRO-DIFFERENTIAL SYSTEM

In this paper, using the differential inequality and singularly perturbed theory, the singularly perturbed boundary value problems for nonlinear integro-differential system has been studied. Under some appropriate assumptions, the existence of solution has been proved and the uniform validness of the asymptotic expansions for arbitrary nth-order have been obtained simply and conveniently.     

THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS

§ 1　 IntroductionA class of singularly perturbed boundary value problems were studied by Mo[1～ 6] .Now we consider the following singularly perturbed nonlinear boundary value problem ofthe formεd2 ydx2 =f(x,y,y′) ,　 0 相似文献   

THE SOLVABILITY FOR NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL SYSTEM

The solvability for the nonlinear singularly perturbed boundary value pro- blem of differential system is considered.Using the boundary layer corrective method the formal asymptotic solution is constructed.And using the theory of differential inequality proves the uniform validity of the asymptotic expansion for the solution.     

非线性积分微分方程组奇摄动边值问题

本文讨论含积分算子的非线性微分方程组Ｒｏｂｉｎ边值问题的奇摄动,在适当假设条件下通过对角化技巧,利用逐步逼近法证明了解的存在,并得到直到Ｏ（ε＾Ｎ＋１）的按范数界限的一致有效估计。     

BOUNDARY VALUE PROBLEMS TO A CLASS OF SINGULARLY PERTURBED NONLINEAR SYSTEM WITH TURNING POINTS

ConsidertheboundaryvalueproblemtothesingularlyperturbednonlinearsystemintheformofwhereEisasmallpositiveparameter,y=(yi,'..)y.),f=(fi,...)fn),A=(Al,'',A.)andB=(BI,sn).MohasdiscussedtheseDroblemsundervarioussituationsusingthemethodofdifferentialinequalities[1--'].Inthispaperweconsiderthecaseoffi.:(0,y,y')=0anduseaclassofnewboundarylayerfunctions.TheoremAssumethat(a)fi(x,y,z)Hfi(x,yi,'',yn,if)''jz.)eC'{xE[~l,1],yie[di,ei],ifER}andtherearepositivenondecreasingcontinuousfunctionsif,i=1,2,'…     

二阶奇摄动拟线性微分系统的可解性

本文研究了一类二阶拟线件微分系统.利用边界层校正法,Green公式以及微分不等式理论,得到了一类一二阶拟线性微分系统两点边值问题的可解性条件.     

THE NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS WITH BOUNDARY PERTURBATION

The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied.     

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。     

A CLASS OF NONLINEAR NONLOCAL SINGULARLY PERTURBED PROBLEMS FOR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION

A class of nonlinear nonlocal singularly perturbed boundary value problems for elliptic equation with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series, the boundary layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems is studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed.     

BOUNDARY AND INTERIOR LAYER PHENOMENA OF SINGULARLY PERTURBED NONLINEAR ELLIPTIC PROBLEMS

This paper investigates the boundary value problems for a class of singularly perturbed nonlinear elliptic equations. By means of the theory of partial differential inequalities the author obtains the existence and asymptotic estimation of the solutions, involving the boundary and interior layer behavior, of the problems as described.     

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…     

MULTIPLE LAYER BEHAVIOR OF BOUNDARY VALUE PROBLEM FOR SINGULARLY PERTURBED n-TH ORDER NONLINEAR DIFFERENTIAL EQUATION

In this paper,we study the singular perturbation of boundary value problem for a class of n-th order nonlinear differential equation,the solution is shown to exhibit multiple layer behavior.According to different layers and by introducing extended variable,we obtain the uniformly effective asymptotic expansion with different boundary layer correction term.     

A KIND OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM FOR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATION

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ASYMPTOTIC SOLUTION TO NONLINEAR REACTION DIFFUSION EQUATION WITH TWO SMALL PARAMETERS

In this paper, a class of nonlinear reaction diffusion singularly perturbed problem with two parameters is studied. Using the singular perturbation method, the structure of solution to the problem is discussed related two small parameters. The asymptotic solution to the problem is given.