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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00461877" target="_blank" >RIV/67985840:_____/16:00461877 - isvavai.cz</a>
Alternative codes found
RIV/00216224:14410/16:00088080
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Solutions of half-linear differential equations in the classes Gamma and Pi
Original language description
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 $alpha=2$.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Difference equations and dynamic equations on time scales III</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)