Methods in half-linear asymptotic theory

0463600 - MÚ 2017 RIV US eng J - Článek v odborném periodiku
Řehák, Pavel
Methods in half-linear asymptotic theory.
Electronic Journal of Differential Equations. Roč. 2016, Č. 267 (2016), s. 1-27. ISSN 1072-6691
Institucionální podpora: RVO:67985840
Klíčová slova: half-linear differential equation * nonoscillatory solution * regular variation
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.954, rok: 2016
http://ejde.math.txstate.edu/Volumes/2016/267/abstr.html

We study asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation $(r(t)|y'|^{alpha-1}sgn y')'=p(t)|y|^{alpha-1}sgn y$, where $r(t)$ and $p(t)$ are positive continuous functions on $[a,infty)$, $alphain(1,infty)$. The aim of this paper is twofold. On the one hand, we show applications of a wide variety of tools, like the Karamata theory of regular variation, the de Haan theory, the Riccati technique, comparison theorems, the reciprocity principle, a certain transformation of dependent variable, and principal solutions. On the other hand, we solve open problems posed in the literature and generalize existing results. The most of our observations is new also in the linear case.
Trvalý link: http://hdl.handle.net/11104/0262746