Oscillatory and spectral analysis of higher-order differential operators

A. Kalybay^a, R. Oinarov<sup>bc

a</sup> KIMEP University, 4 Abay Ave, Almaty, Republic of Kazakhstan
^b Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, 050010 Almaty, Republic of Kazakhstan
^c L.N. Gumilyov Eurasian National University, 13 Kazhymukan St, 010008 Astana, Republic of Kazakhstan

Abstract: In the paper there are investigated the oscillatory properties of a 2nth order differential equation and the spectral properties of a 2nth order di erential operator. These properties are established using the variational method, which relies on verifying a speci c nth order differential inequality. Here, the coe cients of both the equation and the operator are the weights in this inequality. Furthermore, the characterization of the inequality occurs when the weights satisfy conditions, ensuring the existence of a certain combination of boundary values at innity and at zero for the function involved in this inequality.

Keywords and phrases: higher-order differential equation, differential operator, oscillation, non-oscillation, spectrum, variational method, weighted inequality.

MSC: 34C10, 34K08, 26D10

Received: 06.06.2024

Language: English

DOI: 10.32523/2077-9879-2025-16-3-20-41