De Haan type increasing solutions of half-linear differential equations

0429354 - MÚ 2015 RIV US eng J - Článek v odborném periodiku
Řehák, Pavel
De Haan type increasing solutions of half-linear differential equations.
Journal of Mathematical Analysis and Applications. Roč. 412, č. 1 (2014), s. 236-243. ISSN 0022-247X. E-ISSN 1096-0813
Institucionální podpora: RVO:67985840
Klíčová slova: half-linear equation * increasing solution * Beurling slowly varying function * class Gamma * regular variation * rapid variation
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.120, rok: 2014
http://www.sciencedirect.com/science/article/pii/S0022247X13009633

We study asymptotic behavior of eventually positive increasing solutions to the half-linear equation $(r(t)|y'|^{alpha-1}sgn y')'=p(t)|y|^{alpha-1}sgn y$, where $r,p$ are positive continuous functions and $alphain(1,infty)$. We give conditions which guarantee that any such a solution is in the class $Gamma$ (in the de Haan sense). We also discuss regularly varying solutions and connections with a generalized regular variation and other related concepts. The results can be viewed as a half-linear extension of existing statements for linear equations, but in some aspects they are new also in the linear case.
Trvalý link: http://hdl.handle.net/11104/0234482