一类具有转点的二阶半线性奇摄动边值问题

doi:10.3969/j.issn.1000-5641.2023.02.005

华东师范大学学报（自然科学版） ›› 2023, Vol. 2023 ›› Issue (2): 26-33.doi: 10.3969/j.issn.1000-5641.2023.02.005

一类具有转点的二阶半线性奇摄动边值问题

赵敏, 倪明康*()

华东师范大学数学科学学院, 上海　200241

收稿日期:2021-04-21 出版日期:2023-03-25 发布日期:2023-03-23
通讯作者: 倪明康 E-mail:xiaovikdo@163.com
基金资助:
国家自然科学基金(11871217); 上海市科学技术委员会基金(18dz2271000)

A class of second-order semilinear singularly perturbed boundary value problems with turning points

Min ZHAO, Mingkang NI*()

School of Mathematical Sciences, East China Normal University, Shanghai　200241, China

Received:2021-04-21 Online:2023-03-25 Published:2023-03-23
Contact: Mingkang NI E-mail:xiaovikdo@163.com

摘要/Abstract

摘要：

研究了一类具有转点的二阶半线性奇摄动问题解的渐近性. 首先, 给出了在转点附近发生稳定性交替的若干判别准则. 其次, 通过修正退化问题的正则化方程, 提高了原问题渐近解的精度, 并利用Nagumo定理证明了光滑解的存在性. 最后, 通过一个算例验证了结果的正确性.

关键词: 奇摄动, 边值问题, 转点, 稳定性交替, 渐近解

Abstract:

The dynamical behavior of a class of second-order semilinear singularly perturbed Neumann boundary value problems with a turning point are studied. Firstly, we establish sufficient conditions for the exchange of stabilities near the turning point. By correcting the regularized equation of the degenerate problem, the accuracy of the asymptotic solution to the original problem is improved. Secondly, the Nagumo theorem is used to prove the existence of a smooth solution. Finally, a specific example is used to verify the validity of the results.

Key words: singular perturbation, boundary value problems, turning point, exchange of stabilities, asymptotic solution

中图分类号:

O175.14

赵敏, 倪明康. 一类具有转点的二阶半线性奇摄动边值问题[J]. 华东师范大学学报（自然科学版）, 2023, 2023(2): 26-33.

Min ZHAO, Mingkang NI. A class of second-order semilinear singularly perturbed boundary value problems with turning points[J]. Journal of East China Normal University(Natural Science), 2023, 2023(2): 26-33.

图/表 3

参考文献 15

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一类具有转点的二阶半线性奇摄动边值问题

A class of second-order semilinear singularly perturbed boundary value problems with turning points

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