A two point boundary value problem for a singularly perturbed system with double root of the degenerate equation is studied. This is a new class of problem in the case when the nonlinear term at the right end of the system is discontinuous on the straight line, which leads to the formation of complex multizonal internal layers that can be divided into eight regions in the neighborhood of the discontinuous straight line. In this paper, not only the modified boundary layer function method is used to obtain a smooth solution, but also the matching method is used to prove the existence of the solution to the problem. And its remainder estimation is given.

中文翻译：

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一类右边不连续且简并解多重根的奇摄动系统的多尺度研究


研究了简并方程双根奇摄动系统的两点边值问题。这是一类新问题，当系统右端的非线性项在直线上不连续时，会导致形成复杂的多区域内层，这些内层可以在系统的邻域内分为八个区域。不连续的直线。本文不仅采用修正边界层函数法获得光滑解，而且采用匹配方法证明问题解的存在性。并给出了其余数估计。