具有重退化根的奇摄动方程的Neumann边值问题
The Neumann Boundary Value for the Singularly Perturbed Problem with Degenerate Equation Having Double Root
DOI: 10.12677/PM.2018.83039, PDF,    科研立项经费支持
作者: 孙玉娇*, 陈松林：安徽工业大学数理科学与工程学院，安徽 马鞍山
关键词: 奇摄动；重根；边界层函数法；渐近解；Singular Perturbation； Double Root； Boundary Layer Method； Asymptotic Solution
摘要: 研究具有重退化根的二阶奇摄动方程 Neumann 边值问题。在一定条件下利用修正的边界层函数法构造出解的形式渐近展开式，获得更为精确的以指数形式衰减的边界层函数。最后利用上下解方法得到了解的存在性和一致有效估计。
Abstract: The Neumann boundary value for the second order singularly perturbed problem with degenerate question having double root is studied in this paper. Under certain conditions, the method of mod-ified boundary layer function is used to construct the formal asymptotic expansion of the solution and obtain the more precise boundary layer functions which decay exponentially. The existence and uniformly valid approximation of solutions are obtained by upper and lower solutions method.
文章引用：孙玉娇, 陈松林. 具有重退化根的奇摄动方程的Neumann边值问题[J]. 理论数学, 2018, 8(3): 296-303. https://doi.org/10.12677/PM.2018.83039

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