一类高阶非线性边值问题的奇异摄动  

Singular Perturbations for a Class of Boundary Value Problems of Higher Order Nonlinear Differential Equations

作　　者：史玉明[1] 刘光旭[2] 

机构地区：[1]曲阜师范大学数学系,山东曲阜273165 [2]南开大学教学系,天津300071

出　　处：《应用数学和力学》1996年第12期1129-1136,共8页Applied Mathematics and Mechanics

摘　　要：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: e^2y^(n)=f(t,e,y,…,y^(n-2) Pj(ε)y^(j)(0,ε)-qj(ε)y^(j+1)(0,ε)=Aj(ε) (0≤j≤n-3) a_d(ε)y(n-2)(0,ε)-a_2(ε)y^(n-1)(0,ε)=B(ε) b_1(ε)y(n-2)(1,ε)十b_2(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。In this paper, it has been studied that the singular perturbations for the higher order nonlinear boundary value problem of the form by the method of higher order differential inequalities and boundary layer corrections. Under some mild conditions, the existence of the perturbed solution is proved and its uniformly efficient asymptotic expansions up to its nth-order derivative function are given out. Hence, the existing results are extended and improved.

关 键 词：非线性 边值问题 奇摄动 微分不等式 摄动解 

分 类 号：O175.8[理学—数学]