A class of singularly perturbed Robin boundary value problems in critical case

Abstract

This paper discusses a class of nonlinear singular perturbation problems with Robin boundary values in critical cases. By using the boundary layer function method and successive approximation theory, the corresponding asymptotic expansions of small parameters are constructed, and the existence of uniformly efficient smooth solutions is proved. Meanwhile, we give a concrete example to prove the validity of our results.

Keywords

• critical case
• singular perturbation
• boundary function method
• approximate solution
• diagonalization technique