Half-linear differential equations: Regular variation, principal solutions, and asymptotic classes
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Date
2023-01-03
Authors
Řehák, Pavel
ORCID
0000-0002-2452-2204Advisor
Referee
Mark
Journal Title
Journal ISSN
Volume Title
Publisher
Bolyai Institute, University of Szeged
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Abstract
We are interested in the structure of the solution space of second-order half-linear differential equations taking into account various classifications regarding asymptotics of solutions. We focus on an exhaustive analysis of the relations among several types of classes which include the classes constructed with respect to the values of the limits of solutions and their quasiderivatives, the classes of regularly varying solutions, the classes of principal and nonprincipal solutions, and the classes of the so-lutions that obey certain asymptotic formulae. Many of our observations are new even in the case of linear differential equations, and we provide also the revision of existing results.
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Citation
Electronic Journal of Qualitative Theory of Differential Equations. 2023, vol. 2023, issue 1, p. 1-28.
https://www.math.u-szeged.hu/ejqtde/p9954.pdf
https://www.math.u-szeged.hu/ejqtde/p9954.pdf
Document type
Peer-reviewed
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Published version
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Language of document
en