EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 99(113), pp. 125–137 (2016)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home


Pick a mirror



Jaroslav Jaros, Kusano Takasi

Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Bratislava, Slovakia; Department of Mathematics, Faculty of Science, Hiroshima University, Higashi-Hiroshima, Japan

Abstract: For the generalized Thomas–Fermi differential equation
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

Keywords: generalized Thomas–Fermi differential equation; Avakumovic's theorem; positive solutions; asymptotic behavior, regularly varying functions

Classification (MSC2000): 34C11; 26A12

Full text of the article: (for faster download, first choose a mirror)

Electronic fulltext finalized on: 12 Apr 2016. This page was last modified: 20 Apr 2016.

© 2016 Mathematical Institute of the Serbian Academy of Science and Arts
© 2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition