一类具有不连续源的奇摄动半线性微分方程组边值问题

A class of boundary value problem of singular perturbed semi-linear differential systems with discontinuous source term

讨论了一类具有不连续源的奇摄动半线性微分方程组边值问题,构造了形式渐近解.利用Hartman-Nagumo不等式证明了奇摄动半线性微分方程组的解的存在性与唯一性,利用Aumann介值定理,得到了该方程组解的光滑性,并且得到了一致有效估计.

In this paper a class of boundary value problems of the singular perturbed semi-linear differential systems with discontinuous source term is discussed.The formal asymptotic expansion is constructed.Using Hartman-Nagumo inequality,the existence and uniqueness of the solution of the singular perturbed semi-linear differential systems is proved.Using Aumann intermediate theorem,the smoothness of the solution of the systems is obtained.And the uniformly valid estimation for the solution of the systems is obtained.