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Medientyp:
E-Artikel
Titel:
A precise asymptotic description of half‐linear differential equations
Beteiligte:
Řehák, Pavel
Erschienen:
Wiley, 2024
Erschienen in:Mathematische Nachrichten
Sprache:
Englisch
DOI:
10.1002/mana.202200302
ISSN:
0025-584X;
1522-2616
Entstehung:
Anmerkungen:
Beschreibung:
<jats:title>Abstract</jats:title><jats:p>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 Poincaré–Perron solutions. Many of our results are new even in the linear case.</jats:p>