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Singularly perturbed semilinear elliptic boundary value problems with discontinuous source term. (English) Zbl 1353.35034

Summary: 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.

MSC:

35B25 Singular perturbations in context of PDEs
35C20 Asymptotic expansions of solutions to PDEs
35R05 PDEs with low regular coefficients and/or low regular data
35J20 Variational methods for second-order elliptic equations
35J61 Semilinear elliptic equations
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