THE ASYMPTOTIC EXPRESSION OF THE SOLUTION OF THE CAUCHY’S PROBLEM FOR A HIGHER ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION WHEN THE LIMIT EQUATION HAS SINGULARITY

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SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR HIGHER ORDINARY DIFFERENTIAL EQUATION

In this paper we study the singular perturbation of boundary value problems with perturbations both in the operater and in the interval ends. So as to prove the existence and uniqueness of solution of perturbed problem, to establish the asymptotic expression involving three parameters. Thus, the iterative equation of finding the asymptotic solution is derived and the estimation of the remainder term is given out. We extend results of [1]—[5].     

SINGULAR PERTURBATION FOR A CLASS OF SEMILINEAR SECOND ORDER SYSTEMS WITH PERTURBATION BOTH IN BOUNDARY AND IN OPERATOR

We study the boundary value problem where ε, μ are two positive parameters, are n-dimensional vector functions and the boundary is perturbed. This vector boundary problem does not appear to have been studied. Under appropriate assumptions we obtain existence of solution and satisfies where i=1, 2, …, n; Here y_(0,0)~t(t) is a solution of reduced equation f~i (t, y~1, …, y_(0,0)~t,…, y~n, 0, 0)=0, while y_(s-k,k)~i(t) (k=0, 1,…, s; s=1, 2, …, m) can be obtained successively from certain linear systems.     

算子与边界双摄动的非线性方程边值问题的奇摄动

本文应用在边界层构造校正项的方法研究算子与边界摄动相结合的二阶非线性边值问题εx″=g(t,x,ε),μ≤t≤1-μx(t,ε)|_(t-μ)=α(ε,μ)x(t,ε)|_(t-1-μ)=β(ε,μ)的奇摄动,导出解及其导函数的一致有效渐近式和余项的估计,并证明当小参数是充分小时,边值问题的解是存在和唯一.     

Singular perturbation of the fourth order elliptic equation when the limit equation is elliptic-parabolic

3@1In this paper we cosider the singular perturbation of the fourth order elliptic equation-ε~2△~2u y~m(α~2u)/(αy~2) (α~2u)/(αx~2) α(x,y)-(αu)/(αy) b(x,y)(αu)/(αx) c(x,y)=0 when the limit equationis elliptic-parabolic,where εis a positive parameter,m is a positive real number,△isLaplacian operator,a.b.c are sufficiently smooth.Under appropriate condition we derivethe sufficient condition of solvability and prove the existence of solution and give auniformly valid asymptotic solution of arbitrary order.     

Singular perturbation of initial value problem for a nonlinear second order systems

In this paper,the singular perturbation of initial value problem for nonlinearsecond order vector differential equationsε~rx″=f(t,x,x′,ε)x(0,ε)=a,x′(0,ε)=βis discussed,where r>0 is an arbitrary constant,ε>0 is a small parameter,x,f,aandβ∈R~n.Under suitable assumptions,by using the method of many-parameterexpansion and the technique of diagonalization,the existence of the solution of pertur-bation problem is proved and its uniformly valid asymptotic expansion of higher order isderived.     

Singular perturbation of general boundary value problem for nonlinear differential equation system

I.IntroductionAllphysicalsystemsarenonlineartosomeextent.Actually,Lineal.systemisimaginarymodelwherenonlinearfactorisomittedinnonlinearsystem.Insolvingtheautocontl'ol,nonlinearoscillationtheory,theboundarystagnationproblenloffluidIncchanicsandsollleproblemsofsemi-conducttheoryandquantummechanicsetc'.weOnlyncedtosolvethefollowingproblem,whichisnonlineardifferentialequationsystemwithtilesll,allparanletel'inhighestorderderivativeandnonlinearboundaryconditions.whereE>0isasmallparameter,teR,x,fi…     

Singular Perturbation of Boundary Value Problem for Quasilinear Third-Order Ordinary Differential Equations Involving Two Small Parameters

ＩｎｔｒｏｄｕｃｔｉｏｎＡｂｏｕｔｓｉｎｇｕｌａｒｐｅｒｔｕｒｂａｔｉｏｎｏｆｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｆｏｒｓｅｃｏｎｄ＿ｏｒｄｅｒｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｗｏｒｋｓｏｆａｌａｒｇｅｎｕｍｂｅｒｗｅｒｅｃｏｎｓｉｄｅｒｅｄｏｎｌｙｆｏｒｔｈｅｃａｓｅｏｆｉｎｖｏｌｖｉｎｇｏｎｅｓｍａｌｌｐａｒａｍｅｔｅｒ[1- 4].Ｏｎｌｙａｆｅｗｗｏｒｋｓｗｅｒｅｃｏｎｓｉｄｅｒｅｄｆｏｒｔｈｅｃａｓｅｏｆｉｎｖｏｌｖｉｎｇｔｗｏｓｍａｌｌｐａｒａｍｅｔｅｒｓ[5 - 8]…     

SINGULAR PERTURBATION OF GENERAL BOUNDARY VALUE PROBLEM FOR HIGHER ORDER QUASILINEAR ELLIPTIC EQUATION INVOLVING MANY SMALL PARAMETERS

In this paper applying M.I.visik’s and L.A.Lyuster-nik’s asymptotic method and principle of fixed point offunctional analysis,we study the singular perturbation ofgeneral boundary value problem for higher order quasilinearelliptic equation in the case of boundary perturbation com-bined with equation perturbation.we prove the existenceand uniqueness of solution for perturbed problem.We giveits asymptotic approximation and estimation of relatedremainder term.     

SINGULARLY PERTURBED PHENOMENA OF SEMILINEAR SECOND ORDER SYSTEMS

In this paper we consider singular perturbed phenomena of semilinear second order systems, under appropriate assumptions, the existence and asymptotic behavior as ε→0~+ of solution of vector boundary value problem are proved by constructing special invariant regions in which solutions display so-called boundary layer phenomena and angular layer phenomena.