Sufficient conditions on the function $c(t)$ ensuring that the half-linear second order differential equation \[ (|u^\prime |^{p-2} u^\prime )^\prime + c(t)|u(t)|^{p-2} u(t)=0\,, \quad \quad p>1 \] possesses a nontrivial solution having at least two zeros in a given interval are obtained. These conditions extend some recently proved conjugacy criteria for linear equations which correspond to the case $p=2$.
@article{107680,
author = {Sim\'on Pe\v na},
title = {Conjugacy criteria for half-linear differential equations},
journal = {Archivum Mathematicum},
volume = {035},
year = {1999},
pages = {1-11},
zbl = {1054.34055},
mrnumber = {1684518},
language = {en},
url = {http://dml.mathdoc.fr/item/107680}
}
Peňa, Simón. Conjugacy criteria for half-linear differential equations. Archivum Mathematicum, Tome 035 (1999) pp. 1-11. http://gdmltest.u-ga.fr/item/107680/
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