Weighted Second-Order Differential Inequality on Set of Compactly Supported Functions and Its Applications

Aigerim Kalybay, Ryskul Oinarov and Yaudat Sultanaev
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Aigerim Kalybay: Department of Economics, KIMEP University, 4 Abay Ave., Almaty 050010, Kazakhstan
Ryskul Oinarov: Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 5 Munaytpasov St., Nur-Sultan 010008, Kazakhstan
Yaudat Sultanaev: Faculty of Physics and Mathematics, Akmulla Bashkir State Pedagogical University, 3a Oktyabrskoy Revolutsii St., 450000 Ufa, Russia

Mathematics, 2021, vol. 9, issue 21, 1-22

Abstract: In the paper, we establish the oscillatory and spectral properties of a class of fourth-order differential operators in dependence on integral behavior of its coefficients at zero and infinity. In order to obtain these results, we investigate a certain weighted second-order differential inequality of independent interest.

Keywords: weighted inequality; fourth-order differential operator; oscillation; non-oscillation; spectrum discreteness; spectrum positive definiteness; nuclear operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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