Abstract
In this paper we consider the asymptotic behavior of boundary value problems of nonliner systems εy″ = F(t,y,y′ε), −1<t<1, y(−1, ε) = A, y(1, ε) = B when F possesses a generalized turning point at t = 0. The interior layer phenomenon of the problem is discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Neyfeh A. H., Perturbation Methods, John Wiley and Sons, New York
Ackerberg R. C. and O’malley R. E. Jr., Boundary problem exhibiting resonance, Studies in Appl. Maths., 1970, 49(3):277–295
Grasman J. and Martkowsky B. J., A variational approach to singularly perturbed boundary value problems for ordinary and partial differential equations with turning points, SLAMJ. Appl. Math., 1997, 32:588–597
Jiang F.R., On the boundary value problem for a class of ordinary differential equations with turning points, Applied Math and mech., 1980, 1(2):201–212
Jiang F. R., Necessary Conditions for Resonance in Turning Point Problems for Ordinary Differential Equations, Report AM-R 8608
Desamti, Nonmonotone interior layer theory for some singularly perturbed oasillinear boundary value problems with turning point, SIAM J. Math Anal., 1987, 18(2)
Hower F. A., Singularly perturbed nonlinear boundary value problems with turning points, SIAM J. Math. Anal., 1975, 6:644–660
Howes F. A., Singularly perturbed nonlinear boundary value problems with turning points, SIAM J. Math. Anal., 1978, 9(2):250–271
O’Donnell M. A., Boundary and Interior Layer Behavior in Singularly Perturbed Nonlinear Systems, Doctoral Dissertation, Uni. of California at Davis, 1982
Author information
Authors and Affiliations
About this article
Cite this article
Zhang, H., Zhang, H. On the singular perturbation of nonlinear systems with turning points. J. of Shanghai Univ. 3, 77–80 (1999). https://doi.org/10.1007/s11741-999-0035-2
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11741-999-0035-2