Singularly perturbed semilinear elliptic boundary value problems with discontinuous source term

A class of singularly perturbed semilinear elliptic boundary value problems with discontinuous source term on two different domains is considered in this article. The formal asymptotic solution is constructed by using the method of boundary layer functions. Furthermore, the uniform validity of the solutions is proved by using the maximum principle. Finally, as an illustration, an example is presented.