OSCILLATORY AND SPECTRAL ANALYSIS OF HIGHER-ORDER DIFFERENTIAL OPERATORS
Kalybay A. Oinarov R.
January 2025L.N. Gumilyov Eurasian National University
Eurasian Mathematical Journal
2025#16Issue 320 - 41 pp.
In the paper there are investigated the oscillatory properties of a 2nth order differential equation and the spectral properties of a 2nth order differential operator. These properties are established using the variational method, which relies on verifying a specific nth order differential inequality. Here, the coefficients 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 infinity and at zero for the function involved in this inequality.
differential operator , higher-order differential equation , non-oscillation , oscillation , spectrum , variational method , weighted inequality
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KIMEP University, 4Abay Ave, Almaty, Kazakhstan
L.N. Gumilyov Eurasian National University, 13 Kazhymukan St, Astana, 010008, Kazakhstan
Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, Almaty, 050010, Kazakhstan
KIMEP University
L.N. Gumilyov Eurasian National University
Institute of Mathematics and Mathematical Modeling
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