Abstract:

In this paper, the asymptotic behavior of solutions for second-order semi-linear singularly perturbed boundary value problems without normal hyperbolicity is studied. By using the method of boundary layer function, we construct the algebraic boundary layers and hence obtain the uniformly valid asymptotic solution and give the error estimate between the asymptotic and exact solutions via the way of differential inequalities. The correctness of the theoretical result is verified through a typical examples.

Key words: Non-hyperbolicity, Boundary function method, Algebraic decay, Asymptotic solutions