A second-order semi-linear equation's singularly perturbed boundary value problem with nonlinear and infinite boundary value conditions is studied in this paper. By making use of the method of boundary layer functions, the correction functions of the left and right boundary layers, including the exponential and algebra-tic types, are constructed. Thus, the uniformly valid asymptotic solution is derived. Then, based on the theory of the differential inequality, existence of solutions of the boundary value problem is proved and the error estimation between the reduced and the exact solutions is given. By comparing with the numerical integration solution, a typical example is deduced for verifying the correctness of the theoretical result.
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