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

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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 
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     title = {On {Avakumovi\'c's} {Theorem} for {Generalized} {Thomas--Fermi} {Differential} {Equations}},
     journal = {Publications de l'Institut Math\'ematique},
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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. http://geodesic.mathdoc.fr/articles/10.2298/PIM1613125J/

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