Solutions of half-linear differential equations in the classes Gamma and Pi

0461877 - MÚ 2017 RIV US eng J - Journal Article
Řehák, Pavel - Taddei, V.
Solutions of half-linear differential equations in the classes Gamma and Pi.
Differential and Integral Equations. Roč. 29, 7-8 (2016), s. 683-714. ISSN 0893-4983. E-ISSN 0893-4983
Institutional support: RVO:67985840
Keywords : half-linear differential equation * positive solution * asymptotic formula
Subject RIV: BA - General Mathematics
Impact factor: 0.565, year: 2016
http://projecteuclid.org/euclid.die/1462298681

We study asymptotic behavior of (all) positive solutions of the non-oscillatory half-linear differential equation of the form $(r(t)|y'|^ {alpha-1}sgn y')'=p(t)|y|^{alpha-1}sgn y$, where $alphain(1,infty)$ and $r,p$ are positive continuous functions on $[a,infty)$, with the help of the Karamata theory of regularly varying functions and the de Haan theory. We show that increasing resp. decreasing solutions belong to the de Haan class $Gamma$ resp. $Gamma_-$ under suitable assumptions. Further we study behavior of slowly varying solutions for which asymptotic formulas are established. Some of our results are new even in the linear case $alpha=2$.
Permanent Link: http://hdl.handle.net/11104/0261440