%A Huaxiong Chen,Yanyan Wang,Mingkang Ni %T The Contrast Structure for the Singularly Perturbed Problem with Slow-Fast Layers and Discontinuous Righthand Side %0 Journal Article %D 2019 %J Acta mathematica scientia,Series A %R %P 865-874 %V 39 %N 4 %U {http://121.43.60.238/sxwlxbA/CN/abstract/article_15912.shtml} %8 2019-08-26 %X

This paper discusses the contrast structure solution for the singularly perturbed problem with slow-fast layers and discontinuous righthand side. By applying the boundary function method, the asymptotic solution of this problem is constructed. Then using the sewing connection method, the existence of the solution is shown and the asymptotic solution is proved to be uniformly valid. Finally, an example is given to illustrate the main results.