On asymptotic behavior of solutions to Emden-Fowler type higher-order differential equations

Astashova, Irina. "On asymptotic behavior of solutions to Emden-Fowler type higher-order differential equations." Mathematica Bohemica 140.4 (2015): 479-488. <http://eudml.org/doc/271810>.

@article{Astashova2015,
abstract = {For the equation \[ y^\{(n)\}+|y|^\{k\}\mathop \{\rm sgn\} y=0,\quad k>1,\ n=3,4, \] existence of oscillatory solutions \[ y=(x^*-x)^\{-\alpha \} h(\log (x^*-x)),\quad \alpha =\frac\{n\}\{k-1\},\ x<x^*, \] is proved, where $x^*$ is an arbitrary point and $h$ is a periodic non-constant function on $\mathbb \{R\}$. The result on existence of such solutions with a positive periodic non-constant function $h$ on $\mathbb \{R\}$ is formulated for the equation \[ y^\{(n)\}=|y|^\{k\}\mathop \{\rm sgn\} y, \quad k>1,\ n=12,13,14. \]},
author = {Astashova, Irina},
journal = {Mathematica Bohemica},
keywords = {nonlinear ordinary differential equation of higher order; asymptotic behavior of solutions; oscillatory solution},
language = {eng},
number = {4},
pages = {479-488},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On asymptotic behavior of solutions to Emden-Fowler type higher-order differential equations},
url = {http://eudml.org/doc/271810},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Astashova, Irina
TI - On asymptotic behavior of solutions to Emden-Fowler type higher-order differential equations
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 4
SP - 479
EP - 488
AB - For the equation \[ y^{(n)}+|y|^{k}\mathop {\rm sgn} y=0,\quad k>1,\ n=3,4, \] existence of oscillatory solutions \[ y=(x^*-x)^{-\alpha } h(\log (x^*-x)),\quad \alpha =\frac{n}{k-1},\ x<x^*, \] is proved, where $x^*$ is an arbitrary point and $h$ is a periodic non-constant function on $\mathbb {R}$. The result on existence of such solutions with a positive periodic non-constant function $h$ on $\mathbb {R}$ is formulated for the equation \[ y^{(n)}=|y|^{k}\mathop {\rm sgn} y, \quad k>1,\ n=12,13,14. \]
LA - eng
KW - nonlinear ordinary differential equation of higher order; asymptotic behavior of solutions; oscillatory solution
UR - http://eudml.org/doc/271810
ER -