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

Robert Vrabel

Kybernetika (2011)

  • Volume: 47, Issue: 4, page 644-652
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Vrabel, Robert. "Boundary layer phenomenon for three -point boundary value problem for the nonlinear singularly perturbed systems." Kybernetika 47.4 (2011): 644-652. <http://eudml.org/doc/196879>.

@article{Vrabel2011,
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.},
author = {Vrabel, Robert},
journal = {Kybernetika},
keywords = {singularly perturbed systems; three-point boundary value problem; method of lower and upper solutions; controller; singularly perturbed systems; three-point boundary value problem; method of lower and upper solutions; controller},
language = {eng},
number = {4},
pages = {644-652},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Boundary layer phenomenon for three -point boundary value problem for the nonlinear singularly perturbed systems},
url = {http://eudml.org/doc/196879},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Vrabel, Robert
TI - Boundary layer phenomenon for three -point boundary value problem for the nonlinear singularly perturbed systems
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 4
SP - 644
EP - 652
AB - 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.
LA - eng
KW - singularly perturbed systems; three-point boundary value problem; method of lower and upper solutions; controller; singularly perturbed systems; three-point boundary value problem; method of lower and upper solutions; controller
UR - http://eudml.org/doc/196879
ER -

References

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  9. Chang, K. W., Howes, F. A., Nonlinear Singular Perturbation Phenomena: Theory and Applications, Springer-Verlag, New York 1984. (1984) Zbl0559.34013MR0764395
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  14. Vrabel, R., Three point boundary value problem for singularly perturbed semilinear differential equations, E. J. Qualitative Theory of Diff. Equ. 70 (2009), 1–4. (2009) Zbl1195.34030MR2577505

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