应用数学和力学2024，Vol.45Issue(4)：470-489,20.DOI:10.21656/1000-0887.440353
一类具有转点的右端不连续奇摄动边值问题
A Class of Right-Hand Discontinuous Singularly Perturbed Boundary Value Problems With Turning Points
摘要
Abstract
The asymptotic behavior of solutions to a class of right-hand discontinuous 2nd-order semilinear sin-gularly perturbed boundary value problems with turning points was studied.Firstly,the original problem was divided into left and right problems at the discontinuity,the accuracy of the asymptotic solution to the left prob-lem was improved through modification of the regularization equation for the left problem degradation problem,and the existence of the smooth solution to the left problem was proved by means of the Nagumo theorem.Sec-ondly,the solution to the right problem was proved to have a spatial contrast structure,and the asymptotic so-lution to the original problem was obtained through smooth joints at the discontinuity points.Finally,the cor-rectness of the results was verified by an example.关键词
奇摄动/边值问题/转点/右端不连续/空间对照/渐近解Key words
singular perturbation/boundary value problem/turning point/discontinuous right-hand side/spatial contrast structure/asymptotic solution estimation分类
数学引用本文复制引用
帅欣,倪明康..一类具有转点的右端不连续奇摄动边值问题[J].应用数学和力学,2024,45(4):470-489,20.基金项目
国家自然科学基金(12371168) （12371168）
上海市科学技术委员会基金(18dz2271000) （18dz2271000）
