Some asymptotic properties of principal solutions of the half-linear differential equation \[ (a(t)\Phi (x^{\prime }))^{\prime }+b(t)\Phi (x)=0\,, \qquad \mathrm {(*)}\] $\Phi (u)=|u|^{p-2}u$, $p>1$, is the $p$-Laplacian operator, are considered. It is shown that principal solutions of (*) are, roughly speaking, the smallest solutions in a neighborhood of infinity, like in the linear case. Some integral characterizations of principal solutions of (), which completes previous results, are presented as well.
@article{108052,
author = {Mariella Cecchi and Zuzana Do\v sl\'a and Mauro Marini},
title = {Limit and integral properties of principal solutions for half-linear differential equations},
journal = {Archivum Mathematicum},
volume = {043},
year = {2007},
pages = {75-86},
zbl = {1164.34011},
mrnumber = {2310127},
language = {en},
url = {http://dml.mathdoc.fr/item/108052}
}
Cecchi, Mariella; Došlá, Zuzana; Marini, Mauro. Limit and integral properties of principal solutions for half-linear differential equations. Archivum Mathematicum, Tome 043 (2007) pp. 75-86. http://gdmltest.u-ga.fr/item/108052/
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