We consider a third-order singular perturbed differential equation with turning point. The asymptotics of the solution of this equation, which includes the turning point, is constructed.
Similar content being viewed by others
References
R. E. Langer, “On the asymptotic forms of the solutions of ordinary linear differential equations of the third order in a region containing a turning point,” Trans. Amer. Math. Soc., 1955, No. 80, 93–123.
V. N. Bobochko and V. A. Bolilyj, “Pseudodifferential turning point in the theory of singular perturbations,” Nelin. Kolyv., 2, No. 2, 170–176 (1999).
V. O. Bolilyj, “Internal turning point in third-order differential equation,” Mat. Metody Fiz.-Mekh. Polya, 43, No. 3, 44–50 (2000).
V. O. Bolily˘ı and I. O. Zelen´ska, “System of singularly perturbed differential equations with differential internal turning point of the first kind,” Bull. T. Shevchenko Nats. Univ. Kyiv, Ser.: Phys.-Math., 1, No. 1, 41–48 (2014).
W. Wasow, Linear Turning Point Theory, Appl. Math. Sci., Springer-Verlag, New York (1985); https://doi.org/10.1007/978-1-4612-1090-0.
S. A. Lomov, Introduction to the General Theory of Singular Perturbations, Amer. Math. Soc., Providence, RI (1992).
V. M. Bobochko and M. O. Perestyuk, Asymptotic Integration of Liouville Equations with Evolution Points [in Ukrainian], Naukova Dumka, Kyiv (2002).
A. M. Samoilenko and P. F. Samusenko, “Asymptotic integration of singularly perturbed differential algebraic equations with turning points. Part II,” Ukr. Math. J., 73, 988–1007 (2021); https://doi.org/10.1007/s11253-021-01972-5.
A. M. Samoilenko and I. H. Klyuchnyk, “On the asymptotic integration of a linear system of differential equations with a small parameter in the coefficients of some derivatives,” Nelin. Kolyv., 12, No. 2, 208–234 (2009); English translation: Nonlin. Oscill., 12, No. 2, 213–243 (2009).
P. F. Samusenko and M. B. Vira, “Asymptotic solutions of boundary-value problem for singularly perturbed system of differentialalgebraic equations,” Carpathian Math.Publ., 14, 49–60 (2022); https://doi.org/10.15330/cmp.14.1.49-60.
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Neliniini Kolyvannya, Vol. 25, No. 4, pp. 279–290, October–December, 2022.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Bolilyi, V., Sukhovirska, L. Third Order Differential Equation with Turning Point. J Math Sci 277, 187–200 (2023). https://doi.org/10.1007/s10958-023-06827-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06827-x