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

作　　者：赵敏 倪明康 ZHAO Min;NI Mingkang(School of Mathematical Sciences,East China Normal University,Shanghai 200241,China)

机构地区：[1]华东师范大学数学科学学院,上海200241

出　　处：《华东师范大学学报（自然科学版）》2023年第2期26-33,共8页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11871217);上海市科学技术委员会基金(18dz2271000)。

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.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.

关 键 词：奇摄动 边值问题 转点 稳定性交替 渐近解 

分 类 号：O175.14[理学—数学]