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

研究了一类具有转点的右端不连续二阶半线性奇摄动边值问题解的渐近性.首先,在间断处将原问题分为左右两个问题,通过修正左问题退化问题的正则化方程,提高了左问题渐近解的精度,并利用Nagumo定理证明了左问题光滑解的存在性.其次,证明了右问题具有空间对照结构的解,并通过在间断点的光滑缝接,得到了原问题的渐近解.最后,通过一个算例验证了结果的正确性.

The asymptotic behavior of solutions to a class of right-hand discontinuous 2nd-order semilinear singularly 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 problem 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.Secondly,the solution to the right problem was proved to have a spatial contrast structure,and the asymptotic solution to the original problem was obtained through smooth joints at the discontinuity points.Finally,the correctness of the results was verified by an example.