Abstract:

The authors studied boundary layer phenomena for some singularly perturbed Dirichlet problems of secondorder nonlinear equations. Under the principal assumption that a reduced solution is locally weak stable, the existence of solution which exhibits boundary layer behavior was proved  via the method of bounding functions and the theory of differential inequality, with  the asymptotic estimation of solution  given.

Key words: singular perturbation, nonlinear equation, locally weak stability, differential inequality