Singular perturbations in nonlinear boundary value problems

Article type: Research Article

Authors: Shi, Yufeng

Affiliations: School of Mathematics and System Sciences, Shandong University, Jinan 250100, P.R. China

Note: [] This work was partially supported by Foundation for University Key Teacher by Ministry of Education of P.R. China, the National Natural Science Foundation of China Grant 10201018 and Doctor Promotional Foundation of Shandong Grant 02BS127.

Abstract: A class of nonlinear two‐point boundary value problems with singular perturbations are studied. We show asymptotic behavior of the solutions of the perturbed systems and derive asymptotic expansions for the solutions of the perturbed systems, which can approximate the solutions of the perturbed systems as accurately as desired.

Keywords: singular perturbations, asymptotic methods, nonlinear two‐point BVP, boundary layer terms

Journal: Asymptotic Analysis, vol. 34, no. 2, pp. 137-158, 2003