Asymptotics of solutions of the Sturm-Liouville equation in vector-function space

Ya. T. Sultanayev^ab, N. F. Valeev^b, A. Yeskermessuly<sup>c

a</sup> Faculty of Mechanics and Mathematics, Chair of Mathematical Analysis, Center for Applied and Fundamental Mathematics, M.V. Lomonosov Moscow State University, 1 Leninskie gory, 119991 Moscow, Russian Federation
^b Chair of Mathematics and Statistics, M. Akmulla Bashkir State Pedagogical University, 3a October Revolution St, 450000 Ufa, Russian Federation
^c Faculty of Natural Sciences and Informatization, Altynsarin Arkalyk Pedagogical Institute, 17 Auelbekov St, 110300 Arkalyk, Republic of Kazakhstan

Abstract: In this paper, we study the asymptotic behaviour of fundamental systems of solutions to the Sturm-Liouville equation with rapidly oscillating potentials in a two-dimensional vector-function space. We consider di erent cases in which the coe cients do not satisfy the regularity conditions. Additionally, we investigate the asymptotic behaviour of solutions in resonance cases.

Keywords and phrases: asymptotic methods, rapidly oscillating coe cients, vector-function, L-diagonal system, resonance case.

MSC: 34L05, 34E05

Received: 14.06.2024

Language: English

DOI: 10.32523/2077-9879-2025-16-3-90-101