关于n阶微分方程边值问题（Ⅲ）——奇摄动的渐近展开

本文研究n阶非线性过值问题(NB)的奇异摄动。在较一般的条件下,应用高阶微分不等式理论证明了摄动解的存在性,并给出了摄动解直到n阶导函数的一致有效渐近展开式,推广和改进了已有的结果。     

On singularly perturbed quasilinear systems

In this paper, the objective is to give sufficient conditions for the existence of solution of the nonlinear two-point boundary value problem(1.1). And we employ these results to consider the boundary layer phenomena of the quasilinear weakly coupled singularly perturbed system (DP)_q.     

SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS

ＳＩＮＧＵＬＡＲ　ＰＥＲＴＵＲＢＡＴＩＯＮＳ　ＦＯＲ　Ａ　ＣＬＡＳＳ　ＯＦ　ＢＯＵＮＤＡＲＹ　ＶＡＬＵＥ　ＰＲＯＢＬＥＭＳ　ＯＦ　ＨＩＧＨＥＲ　ＯＲＤＥＲ　ＮＯＮＬＩＮＥＡＲ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳＳｈｉＹｕａｎｉｎｇ（史玉明）...     

Boundary and angular layer behavior in singularly perturbed semilinear systems

Some authors employed the method and technique of differential inequalities to obtain fairly general results concerning the existence and asymptotic behavior, as ε→n~+, of the solutions of scalar boundary value problems In this paper, we extend these results to vector boundary value problems, under analogous stability conditions on the solution u=u(t) of the reduced equation O=h(t, u) Two types of asymptotic behavior are studied, depending on whether the reduced solution u(t) has or does not have a con tinuous first derivative in (a, b) leading to the phenomena of boundary and angular layers.     

ON SINGULARLY PERTURBED QUASILINEAR SYSTEMS

In this paper, the objective is to give sufficient conditions for the existence of solutionof the nonlinear two-point boundary value problem(1.1). And we employ these-results toconsider the boundary layer phenomena of the quasilinear weakly coupled singularlyperturbed system(DP)_q.     

关于n阶微分方程的混合边值问题（Ⅰ）—存在定理

本文应用微分不等式方法和技巧研究一般n阶微分方程的混合边值问题,得到边值问题(1.2)的解的存在定理.     

奇摄动半线性系统的边界层和角层性质

一些作者已对纯量边值问题εy"=h(t,y),a相似文献   

关于奇摄动拟线性系统

本文目的在于对非线性两点边值问题(1.1)证明其解存在的充分条件。并利用这一结果研究拟线性弱耦合奇摄动系统(DP)q的边界层现象。     

一类高阶非线性边值问题的奇异摄动

本文应用高阶微分不等式技巧和边界层校正法研究一类高阶非线性方程混合边值问题: e2yn=f(t,e,y,…,yn-2 Pj(ε)yj(0,ε)-qj(ε)yj+1(0,ε)=Aj(ε)(0≤j≤n-3)a₁(ε)y(n-2)(0,ε)-a₂(ε)yn-1(0,ε)=B(ε)b₁(ε)y(n-2)(1,ε)十b₂(ε)y(n-1)(1,ε)=C(ε)的奇异摄动。在较一般的条件下,证明了摄动解的存在性,并得到了摄动解直到n阶导函数的一致有效渐近展开式,从而推广和改进了前人的结果。