Geodesic
On asymptotic behavior of solutions to Emden-Fowler type higher-order differential equations
Mathematica Bohemica, Tome 140 (2015) no. 4, pp. 479-488.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

For the equation $$ y^{(n)}+|y|^{k}\mathop {\rm sgn} y=0,\quad k>1,\ n=3,4, $$ existence of oscillatory solutions $$ y=(x^*-x)^{-\alpha } h(\log (x^*-x)),\quad \alpha =\frac {n}{k-1},\ x^*, $$ 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 $$ y^{(n)}=|y|^{k}\mathop {\rm sgn} y, \quad k>1,\ n=12,13,14. $$
DOI : 10.21136/MB.2015.144464
Classification : 34C10, 34C15
Keywords: nonlinear ordinary differential equation of higher order; asymptotic behavior of solutions; oscillatory solution 
@article{10_21136_MB_2015_144464,
     author = {Astashova, Irina},
     title = {On asymptotic behavior of solutions to {Emden-Fowler} type higher-order differential equations},
     journal = {Mathematica Bohemica},
     pages = {479--488},
     publisher = {mathdoc},
     volume = {140},
     number = {4},
     year = {2015},
     doi = {10.21136/MB.2015.144464},
     mrnumber = {3432547},
     zbl = {06537678},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2015.144464/}
}
TY  - JOUR
AU  - Astashova, Irina
TI  - On asymptotic behavior of solutions to Emden-Fowler type higher-order differential equations
JO  - Mathematica Bohemica
PY  - 2015
SP  - 479
EP  - 488
VL  - 140
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2015.144464/
DO  - 10.21136/MB.2015.144464
LA  - en
ID  - 10_21136_MB_2015_144464
ER  - 
%0 Journal Article
%A Astashova, Irina
%T On asymptotic behavior of solutions to Emden-Fowler type higher-order differential equations
%J Mathematica Bohemica
%D 2015
%P 479-488
%V 140
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2015.144464/
%R 10.21136/MB.2015.144464
%G en
%F 10_21136_MB_2015_144464
Astashova, Irina. On asymptotic behavior of solutions to Emden-Fowler type higher-order differential equations. Mathematica Bohemica, Tome 140 (2015) no. 4, pp. 479-488. doi : 10.21136/MB.2015.144464. http://geodesic.mathdoc.fr/articles/10.21136/MB.2015.144464/

Cité par Sources :