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OSCILLATORY AND SPECTRAL PROPERTIES OF A CLASS OF FOURTH-ORDER DIFFERENTIAL OPERATORS VIA A NEW HARDY-TYPE INEQUALITY
L. N. Gumilyov Eurasian National University, Kazakhstan.
KIMEP University, Kazakhstan.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). UiT The Arctic University of Norway, Norway.ORCID iD: 0000-0002-5914-3247
2024 (English)In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 27, no 1, p. 63-83Article in journal (Refereed) Published
Abstract [en]

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.
Place, publisher, year, edition, pages
ELEMENT , 2024. Vol. 27, no 1, p. 63-83
Keywords [en]
Inequalities, second-order Hardy-type inequality, weights, fourth-order differential equation, differential operator, oscillation, non-oscillation, spectral properties, variational method
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-98699DOI: 10.7153/mia-2024-27-05ISI: 001158242800001Scopus ID: 2-s2.0-85187671783OAI: oai:DiVA.org:kau-98699DiVA, id: diva2:1841083
Available from: 2024-02-27 Created: 2024-02-27 Last updated: 2024-04-05Bibliographically approved

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Persson, Lars-Erik

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