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Zbl 1212.34027
Lin, Xiaojie; Liu, Wenbin
Singular perturbation of a second-order three-point boundary value problem for nonlinear systems. (English)
[J] J. Shanghai Univ. 13, No. 1, 16-19 (2009). ISSN 1007-6417; ISSN 1863-236X/e

Summary: This paper deals with the existence of solutions to a singularly perturbed second-order three-point boundary value problem for nonlinear differential systems. The authors construct an appropriate generalized lower- and upper-solution pair and employ the Nagumo conditions and algebraic boundary layer functions to ensure the existence of solutions to the problem. The uniformly valid asymptotic estimate of the solutions is given as well. The differential systems have nonlinear dependence on all order derivatives of the unknown.

MSC 2000:: *34B10 Multipoint boundary value problems
34E05 Asymptotic expansions (ODE)
34B15 Nonlinear boundary value problems of ODE
34E20 Asymptotic singular perturbations, methods (ODE)

Keywords: singular perturbation; nonlinear systems; three-point boundary value problem; upper and lower solutions

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