Abstract: We consider a class of singularly perturbed quasilinear differential equation with Robin boundary value conditions and discontinuous right-hand side. Firstly, under the given conditions, the asymptotic expression of a smooth solution with an internal layer in the neighborhood of the discontinuous curve is constructed. Secondly, based on the matching technique, the existence of such solution is proved, and the remainder estimation is given. Finally, the effectiveness of the method is verified by a numerical example.

Key words: singular perturbation, asymptotic expansion, internal layer, Robin boundary value condition