SINGULAR PERTURBATION OF NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper we consider the boundary value problem where ε.μ are two positive parameters. Under f_y≤-k<0 and other suitable restrictions, there exists a solution and it satisfied where y_(0,0)(x) is solution of reduced problem while y_i-j,j(x)(j=0,1,...,i;i=1,2,...,m) can be obtained successively from certain linear equations.     

Singularly perturbed phenomena of semilinear second order systems

In this paper we consider singular perturbed phenomena of semilinear second ordersystems, under appropriate assumptions, the existence and asymptotic behavior asε→0⁺ of solution of vector boundary value problem are proved by constructing specialinvariant regions in which solutions display so-called boundary layer phenomena andangular layer phenomena.     

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

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

非线性边值问题的奇摄动

本文研究边值问题:εy"=f(x,y,y',ε,μ)(μ0(ε,μ)y(x,ε,μ)|(x=1-μ)=φ₁(ε,μ)其中ε,μ是两个正的小参数 在f_y’≤-k<0和其他适当的限制下,存在一个解且满足其中y₀,0(x)是退化问题 f(x,y,y',0,0)=0(01(0,0)的解,而y_i-j,j(x)(j=0,1,…,i;i=1,2,…m)能够从某些线性方程逐次求得.     

极限方程为退缩椭圆型的一类三阶偏微分方程边值问题的奇摄动

本文研究极限方程在部分边界上为椭圆—抛物的一类三阶偏微分方程第一边值问题ε[(?)~3u]/[(?)y~3]-[y(?)~2u]/[(?)x~2]-[(?)~2u]/[(?)y~2]-a(x,y)[(?)u]/[(?)x]-b(x,y)[(?)u]/[(?)y]-c(x,y)u=f(x,y),u|_Γ=0,[(?)u]/[(?)y]|_(y=β)=0的奇摄动,在适当的假设下,证得解的存在并给出任意阶的一致有效的渐近展开式.     

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.     

某类二阶非线性系统初值问题的奇摄动*

本文研究某类二阶非线性向量微分方程初值问题ε'x"=f(t,x,x',ε),x(0,ε)=a,x'(0,ε)=β的奇摄动,其中r>0为任意常数,ε>0为小参数,x,f,α,β∈Rn.在适当的假设下,利用多参数展开法和对角化技巧,证得摄动问题解的存在和导出解的高阶的一致有效渐近展开式.     

微分算子和边界双摄动的高阶椭圆型方程的狄立克雷问题

本文研究了在边界和算子摄动相结合的情况下高阶椭圆型方程解的渐近式的构造.如果非摄动问题A₀不在谱上,则摄动问题A_ε的渐近解可按小参数ε的次幂展开;如果A₀在谱上,则在A_ε的渐近解中出现有小参数ε的负幂;同时给出了有关的余项的估计.     

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.     

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…