Abstract:

This paper considers second-order semi-linear non-autonomous singularly perturbed boundary value problem under the non-hyperbolic condition. Firstly, we construct the algebraic decay boundary layers by using the method of boundary layer functions. Hence, we obtain the uniformly valid asymptotic solution. Then, based on the obtained asymptotic solution, we define a couple of upper and lower solutions suitably, and prove the existence of solutions, the uniform validity of the asymptotic solution as well as the error estimate between the asymptotic and the exact solutions. Finally, a typical example is performed to verify the correctness of the theoretical result.

Key words: Boundary function method, Algebraic decay, Asymptotic solutions