## 留言板

 引用本文: 史玉明, 刘光旭. 一类高阶非线性边值问题的奇异摄动[J]. 应用数学和力学, 1996, 17(12): 1129-1136.
Shi Yuaning, Liu Guangxu. Singular Perturbations for a Class of Boundary Value Problems of Higher Order Nonlinear Differential Equations[J]. Applied Mathematics and Mechanics, 1996, 17(12): 1129-1136.
 Citation: Shi Yuaning, Liu Guangxu. Singular Perturbations for a Class of Boundary Value Problems of Higher Order Nonlinear Differential Equations[J]. Applied Mathematics and Mechanics, 1996, 17(12): 1129-1136.

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

• 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: 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。
•  [1] K.W.Chang and F.A.Howes,Nonlinear Singular Perturbation Phenomena: Theory and Applications,Springer-Verlag,New York/Berlin/Heidelberg/Tokyo(1984). [2] M.A.O'Donnell,Boundary and corner layer behavior in singularly perturbed semilinear systems boundary value problems,SIAM J.Math.Anal.,2(1984),317-332. [3] 周钦德、李勇,奇异摄动边值问题的渐近展开,应用数学和力学,10(6)(1989),553-557 [4] F.A.Howes,Differential inequalities of higher order and the asymptotic solution of nonlinear boundary value problems,SIAM J.Marlr.Anal.,13(1982),61-80. [5] J.W.Heidel,A second-order nonlinear boundary value problem,J.Math.Anal.Appl.,48(1974),493-503. [6] L.K.Jackson,Subfunctions and second-order ordinary differential inequalities,Adv.in Math.,2(1968),308-363. [7] 史玉明、刘光旭,关于n阶微分方程的混合边值问题(I)—存在定理,高校应用数学学报,6(1991),581-594.
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##### 出版历程
• 收稿日期:  1994-04-10
• 修回日期:  1995-06-28
• 刊出日期:  1996-12-15

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