A precise asymptotic description of half-linear differential equations

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Mathematische Nachrichten 2023 Rehak A precise asymptotic description of halflinear differential equations.pdf(488.83 KB)
Date
2024-04-08
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ORCID
0000-0002-2452-2204
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Referee
Mark
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Publisher
WILEY-V C H VERLAG GMBH
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Abstract
We study asymptotic behavior of solutions of nonoscillatory second-order half-linear differential equations. We give (in some sense optimal) conditions that guarantee generalized regular variation of all solutions, where no sign condition on the potential is assumed. For all of these solutions, we establish precise asymptotic formulas, where positive as well as negative potential is considered. We examine, as consequences, also equations with regularly varying coefficients, or with the coefficients viewed as perturbations of exponentials, or the equations under certain critical (double roots) settings. We make also asymptotic analysis of Poincare-Perron solutions. Many of our results are new even in the linear case.
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Keywords
asymptotic formula, half-linear differential equation, nonoscillatory solution, Poincare-Perron solution, regular variation
Citation
Mathematische Nachrichten. 2024, vol. 297, issue 4, p. 1275-1309.
https://onlinelibrary.wiley.com/doi/10.1002/mana.202200302
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Peer-reviewed
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Language of document
en
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Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
DOI
10.1002/mana.202200302
URI
https://hdl.handle.net/11012/245540
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