Regular half-linear second order differential equations
Archivum Mathematicum (2003)
- Volume: 039, Issue: 3, page 233-245
- ISSN: 0044-8753
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topDošlý, Ondřej, and Řezníčková, Jana. "Regular half-linear second order differential equations." Archivum Mathematicum 039.3 (2003): 233-245. <http://eudml.org/doc/249117>.
@article{Došlý2003,
abstract = {We introduce the concept of the regular (nonoscillatory) half-linear second order differential equation \[ \left(r(t)\Phi (x^\{\prime \})\right)^\{\prime \}+c(t)\Phi (x)=0\,,\quad \Phi (x):=|x|^\{p-2\}x\,,\quad p>1 \qquad \mathrm \{\{(*)\}\}\]
and we show that if (*) is regular, a solution $x$ of this equation such that $x^\{\prime \}(t)\ne 0$ for large $t$ is principal if and only if \[ \int ^\infty \frac\{dt\}\{r(t)x^2(t)|x^\{\prime \}(t)|^\{p-2\}\}=\infty \,. \]
Conditions on the functions $r,c$ are given which guarantee that (*) is regular.},
author = {Došlý, Ondřej, Řezníčková, Jana},
journal = {Archivum Mathematicum},
keywords = {regular half-linear equation; principal solution; Picone’s identity; Riccati-type equation; principal solution; Picone's identity; Riccati-type equation},
language = {eng},
number = {3},
pages = {233-245},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Regular half-linear second order differential equations},
url = {http://eudml.org/doc/249117},
volume = {039},
year = {2003},
}
TY - JOUR
AU - Došlý, Ondřej
AU - Řezníčková, Jana
TI - Regular half-linear second order differential equations
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 3
SP - 233
EP - 245
AB - We introduce the concept of the regular (nonoscillatory) half-linear second order differential equation \[ \left(r(t)\Phi (x^{\prime })\right)^{\prime }+c(t)\Phi (x)=0\,,\quad \Phi (x):=|x|^{p-2}x\,,\quad p>1 \qquad \mathrm {{(*)}}\]
and we show that if (*) is regular, a solution $x$ of this equation such that $x^{\prime }(t)\ne 0$ for large $t$ is principal if and only if \[ \int ^\infty \frac{dt}{r(t)x^2(t)|x^{\prime }(t)|^{p-2}}=\infty \,. \]
Conditions on the functions $r,c$ are given which guarantee that (*) is regular.
LA - eng
KW - regular half-linear equation; principal solution; Picone’s identity; Riccati-type equation; principal solution; Picone's identity; Riccati-type equation
UR - http://eudml.org/doc/249117
ER -
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Citations in EuDML Documents
top- Mariella Cecchi, Zuzana Došlá, Mauro Marini, Limit and integral properties of principal solutions for half-linear differential equations
- Ondřej Došlý, Zuzana Pátíková, Hille-Wintner type comparison kriteria for half-linear second order differential equations
- Zuzana Pátíková, Hartman-Wintner type criteria for half-linear second order differential equations
- Ondřej Došlý, Jaroslav Jaroš, A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations
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