OSCILLATORY AND SPECTRAL PROPERTIES OF A CLASS OF FOURTH–ORDER DIFFERENTIAL OPERATORS VIA A NEW HARDY–TYPE INEQUALITY
Oinarov R. Kalybay A. Persson L.-E.
January 2024Element D.O.O.
Mathematical Inequalities and Applications
2024#27Issue 163 - 83 pp.
In this paper, we study oscillatory properties of a fourth-order differential equation and spectral properties of a corresponding differential operator. These properties are established by first proving a new second-order Hardy-type inequality, where the weights are the coefficients of the equation and the operator. This new inequality, in its turn, is established for functions satisfying certain boundary conditions that depend on the boundary behavior of one of its weights at infinity and at zero.
differential operator , fourth-order differential equation , Inequalities , non-oscillation , oscillation , second-order Hardy-type inequality , spectral properties , variational method , weights
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L. N. Gumilyov Eurasian National University, 2 Satpayev Str., Astana, 010008, Kazakhstan
KIMEP University, 4 Abay Ave., Almaty, 050010, Kazakhstan
UiT The Arctic University of Norway, PO Box 6050 Langnes, Tromsø, N-9037, Norway
Karlstad University, 2 Universitetsgatan, Karlstad, 651 88, Sweden
L. N. Gumilyov Eurasian National University
KIMEP University
UiT The Arctic University of Norway
Karlstad University
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