Abstract
In this paper we study the boundary value problems for a class of ordinary differential equations with turning points by the method of multiple scales. The paradox in [1] and the variational approach in [2] are avoided. The uniformly valid asymptotic approximations of solutions have been constructed. We also study the case which does not exhibit resonance.
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Ackerberg, R. C., and O'Malley, R. E. Jr, Boundary layer problem exhibiting resonance, Studies inAppl. Math., 49, 3. (1970), 277–295.
Grasman, J., and Matkowsky, B. J., A variational approach to singularly perturbed boundary value problems for ordinary and partial differential equations with turning points,S I AM J. Appl. Math., 32, 3, (1977), 588–597.
Nayfeh, A. H.,Perturbation Methods, Wiley, New York, (1973).
Cook, L. P., and Eckhaus, W., Resonance in a boundary value problem of singular perturbation type, Studies inAppl. Math., 52., 2, (1973), 129–139.
Matkowsky, B. J., On boundary layer problem exhibiting resonance,S I AM Rev. 17, 1, (1975), 82–100.
Niijima, K., On the behavior of solutions of a singularly perturbed boundary value problems with a turning point,S I AM J. Math. Anal., 9, 2 (1973), 298
Olver, F. W. J., Sufficient conditions for Ackerberg-O'Malley resonance,S I AM J. Math. Anal., 9, 2, (1978), 328–355.
Protter M. H., and Weinberger, H. F.,Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, (1967).
Вишик, М. И., и Люстерник, Л. А., Регулярное вырождение и пограничный слой для линейных дифферендиальных уравнений с малым параметром, УМН 12, 5, (1957), 3–122.
O'Malley, R. E., Jr.,Introduction to Singular Perturbations, Acad. Press, New York and London, (1974).
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Fu-ru, J. On the boundary value problems for a class of ordinary differential equations with turning points. Appl Math Mech 1, 211–223 (1980). https://doi.org/10.1007/BF01876745
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DOI: https://doi.org/10.1007/BF01876745