Kybernetika 47 no. 4, 644-652, 2011

Boundary layer phenomenon for three-point boundary value problem for the nonlinear singularly perturbed systems

Robert Vrabel

Abstract:

This paper deals with the three-point boundary value problem for the nonlinear singularly perturbed second-order systems. Especially, we focus on an analysis of the solutions in the right endpoint of considered interval from an appearance of the boundary layer point of view. We use the method of lower and upper solutions combined with analysis of the integral equation associated with the class of nonlinear systems considered here.

Keywords:

singularly perturbed systems, three-point boundary value problem, method of lower and upper solutions, controller

Classification:

93C10, 34E15, 34A34, 34A40, 34B10

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