# Limit and integral properties of principal solutions for half-linear differential equations

Archivum Mathematicum (2007)

• Volume: 043, Issue: 1, page 75-86
• ISSN: 0044-8753

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## Abstract

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Some asymptotic properties of principal solutions of the half-linear differential equation ${\left(a\left(t\right)\Phi \left({x}^{\text{'}}\right)\right)}^{\text{'}}+b\left(t\right)\Phi \left(x\right)=0\phantom{\rule{0.166667em}{0ex}},\phantom{\rule{2.0em}{0ex}}\left(*\right)$$\Phi \left(u\right)={|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.

## How to cite

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Cecchi, Mariella, Došlá, Zuzana, and Marini, Mauro. "Limit and integral properties of principal solutions for half-linear differential equations." Archivum Mathematicum 043.1 (2007): 75-86. <http://eudml.org/doc/250159>.

@article{Cecchi2007,
abstract = {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.},
author = {Cecchi, Mariella, Došlá, Zuzana, Marini, Mauro},
journal = {Archivum Mathematicum},
keywords = {half-linear equation; principal solution; limit characterization; integral characterization; half-linear equation; principal solution; limit characterization; integral characterization},
language = {eng},
number = {1},
pages = {75-86},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Limit and integral properties of principal solutions for half-linear differential equations},
url = {http://eudml.org/doc/250159},
volume = {043},
year = {2007},
}

TY - JOUR
AU - Cecchi, Mariella
AU - Došlá, Zuzana
AU - Marini, Mauro
TI - Limit and integral properties of principal solutions for half-linear differential equations
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 1
SP - 75
EP - 86
AB - 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.
LA - eng
KW - half-linear equation; principal solution; limit characterization; integral characterization; half-linear equation; principal solution; limit characterization; integral characterization
UR - http://eudml.org/doc/250159
ER -

## References

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