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Singular perturbation of a second-order three-point boundary value problem for nonlinear systems. (English) Zbl 1212.34027
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:
34B10Nonlocal and multipoint boundary value problems for ODE
34E05Asymptotic expansions (ODE)
34B15Nonlinear boundary value problems for ODE
34E20Asymptotic singular perturbations, turning point theory, WKB methods (ODE)
References:
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