Multiscale study on a class of singularly perturbed system with discontinuous right-hand side and multiple root of the degenerate solution

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.