一类非线性三阶奇摄动边值问题解的存在性和渐近估计
Existence and Asymptotic Estimates of Solutions for a Class of Nonlinear Third-Order Singularly Perturbed Boundary Value Problems

作者: 张瑞燕 :西北师范大学数学与统计学院,甘肃 兰州;

关键词: 三阶奇异摄动存在性渐近估计Third-Order Singularly Perturbed Existence Asymptotic Estimates

摘要:
本文研究一类三点边值条件下非线性三阶奇摄动边值问题 解的存在性和渐近估计, 其中0 < η < 1,0 < ξη < 1. 通过构造一个恰当的广义上下解对和运用Nagumo 条件和边界层函数,我们得到上述问题解的存在性,并且给出了解的一致有效渐近估计.

Abstract: This paper is devoted to study the existence and asymptotic estimates of solutions for a class of nonlinear third-order singularly perturbed boundary value problems with three-point boundary value conditions where 0 < η < 1, 0 < ξη < 1. By constructing an appropriate generalized upper- and lower-solution pair and employing the Nagumo conditions and boundary layer functions, we obtain the existence of solutions to the above problem and give uniformly valid asymptotic estimates of the solutions.

文章引用: 张瑞燕 (2021) 一类非线性三阶奇摄动边值问题解的存在性和渐近估计。 理论数学, 11, 979-989. doi: 10.12677/PM.2021.116112

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