Geodesic
On Avakumović's Theorem for Generalized Thomas--Fermi Differential Equations
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 125

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

For the generalized Thomas--Fermi differential equation \[ (|x'|^{lpha-1}x')'=q(t)|x|^{\beta-1}x, \] it is proved that if $1 \leq \alpha\beta$ and $q(t)$ is a regularly varying function of index $\mu$ with $\mu>-\alpha-1$, then all positive solutions that tend to zero as $t\to\infty$ are regularly varying functions of one and the same negative index $\rho$ and their asymptotic behavior at infinity is governed by the unique definite decay law. Further, an attempt is made to generalize this result to more general quasilinear differential equations of the form \[ (p(t)|x'|^{lpha-1}x')'=q(t)|x|^{\beta-1}x. \]
DOI : 10.2298/PIM1613125J
Classification : 34C11 26A12
Keywords: generalized Thomas--Fermi differential equation, Avakumović's theorem, positive solutions, asymptotic behavior, regularly varying functions 
@article{10_2298_PIM1613125J,
     author = {Jaroslav Jaro\v{s} and Kusano Taka\^{s}i},
     title = {On {Avakumovi\'c's} {Theorem} for {Generalized} {Thomas--Fermi} {Differential} {Equations}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {125 },
     publisher = {mathdoc},
     volume = {_N_S_99},
     number = {113},
     year = {2016},
     doi = {10.2298/PIM1613125J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM1613125J/}
}
TY  - JOUR
AU  - Jaroslav Jaroš
AU  - Kusano Takaŝi
TI  - On Avakumović's Theorem for Generalized Thomas--Fermi Differential Equations
JO  - Publications de l'Institut Mathématique
PY  - 2016
SP  - 125 
VL  - _N_S_99
IS  - 113
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM1613125J/
DO  - 10.2298/PIM1613125J
LA  - en
ID  - 10_2298_PIM1613125J
ER  - 
%0 Journal Article
%A Jaroslav Jaroš
%A Kusano Takaŝi
%T On Avakumović's Theorem for Generalized Thomas--Fermi Differential Equations
%J Publications de l'Institut Mathématique
%D 2016
%P 125 
%V _N_S_99
%N 113
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM1613125J/
%R 10.2298/PIM1613125J
%G en
%F 10_2298_PIM1613125J
Jaroslav Jaroš; Kusano Takaŝi. On Avakumović's Theorem for Generalized Thomas--Fermi Differential Equations. Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 125 . doi: 10.2298/PIM1613125J

Cité par Sources :