Share This Article:

Asymptotic Estimates for Second-Order Parameterized Singularly Perturbed Problem

Abstract Full-Text HTML Download Download as PDF (Size:886KB) PP. 1988-1992
DOI: 10.4236/am.2014.513191    3,164 Downloads   3,902 Views   Citations
Author(s)    Leave a comment


The boundary value problem (BVP) for parameterized singularly perturbed second order nonlinear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivatives have been established. An example supporting the theoretical analysis is presented.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Kudu, M. (2014) Asymptotic Estimates for Second-Order Parameterized Singularly Perturbed Problem. Applied Mathematics, 5, 1988-1992. doi: 10.4236/am.2014.513191.


[1] Pomentale, T. (1976) A Constructive Theorem of Existence and Uniqueness for the Problem. Zeitschrift für Angewandte Mathematik und Mechanik, 56, 387-388.
[2] Goma, I.A. (1977) Method of Successive Approximations in a Two-Point Boundary Problem with Parameter. Ukrainian Mathematical Journal, 29, 594-599.
[3] Jankowski, T. (2001) Monotone ?terations for Differential Problems. Miskolc Mathematical Notes, 2, 31-38.
[4] Jankowski, T. and Lakshmikantham, V. (1997) Monotone Iterations for Differential Equations with a Parameter. Journal of Applied Mathematics and Stochastic Analysis, 10, 273-278.
[5] Jankowski, T. (1999) Generalization of the Method of Quasilinearization for Differential Problems with a Parameter, Dynamic Systems an Applications, 8, 53-72.
[6] Rontó, M. and Csikos-Marinets, T. (2000) On the Investigation of Some Non-Linear Boundary Value Problems with Parameters. Miskolc Mathematical Notes, 1, 157-166.
[7] Rontó, M. (2000) On Non-Linear Boundary Value Problems Containing Parameters. Archivum Mathematicum, 36, 585-593.
[8] Staněk, S. (1997) Nonlinear Boundary Value Problem for Second Order Differential Equations Depending on a Parameter. Mathematica Slovaca, 47, 439-449.
[9] Zhang, P. (2011) Existence of Positive Solutions for Nonlocal Second-Order Boundary Value Problem with Variable Parameter in Banach Spaces. Fixed Point Theory and Applications, 43, 1687-1812.
[10] Fěckan, M. (1994) Parametrized Singularly Perturbed Boundary Value Problems. Journal of Mathematical Analysis and Applications, 188, 426-435.
[11] Amiraliyev, G.M., Kudu M. and Duru, H. (2004) F?n?te-Difference Method for Parameter?zed S?ngularly Pertur Bed Problem. Journal of Applied Mathematics, 3, 191-199.
[12] Amiraliyev, G.M., Kudu M. and Duru, H. (2006) Uniform Difference Method for a Parameterized Singular Pertur Bation Problem. Applied Mathematics and Computation, 175, 89-100.
[13] Amiraliyeva I.G. and Amiraliyev, G.M. (2009) Uniform Difference Method for Parameterized Singularly Pertur Bed Delay Differential Equations. Numerical Algorithms, 52, 509-552.
[14] Turkyilmazoglu, M. (2011) Analytic Approximate Solutions of Parameterized Unperturbed and Singularly Perturbed Boundary Value Problems. Applied Mathematical Modelling, 35, 3879-3886.
[15] Nayfeh, A.H. (1981) Introduction to Perturbation Techniques. JohnWiley & Sons, New York.
[16] O’Malley Jr., R.E. (1991) Singular Perturbation Methods for Ordinary Differential Equations. Springer-Verlag, New York.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.