Abstract
We propose a method for constructing asymptotic representations of solutions of linear degenerate second-order ordinary differential equations, which permits one to construct exact asymptotics of solutions in a neighborhood of the degeneracy point. An example where one finds a power-law asymptotics is given.
This is a preview of subscription content, log in via an institution to check access.
References
V. P. Glushko, Linear Degenerating Differential Equations (Voronezh. Gos. Univ., Voronezh, 1972) [in Russian].
N. Kh. Rozov, V. G. Sushko, and D. I. Chudova, “Differential equations with degenerate coefficient of the highest-order derivative,” Fundam. Prikl. Mat. 4 (3), 1063–1095 (1998).
V. P. Arkhipov, “Linear second-order differential equations with degenerating coefficient of the second derivative,” Differ. Equ. 47 (10), 1397–1407 (2011).
V. P. Arkhipov and A. V. Glushak, “Degenerate differential equations of the second order. Asymptotic representations of solutions,” Nauchn. Vedom. Belgorod. Gosud. Univ. Mat. Fiz. 44 (20 (241)), 5–22 (2016).
Funding
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors of this work declare that they have no conflicts of interest.
Additional information
Translated from Prikladnaya Matematika i Fizika, 2023, Vol. 55, No. 3, pp. 197–206.
Publisher’s note. Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Arkhipov, V.P., Glushak, A.V. First Asymptotics of Solutions of Degenerate Second-Order Differential Equations. Math Notes 114, 1107–1117 (2023). https://doi.org/10.1134/S0001434623110445
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434623110445