Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, 61662 Brno, Czech Republic
Copyright © 2011 Pavel Řehák. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linear
, with , with , to behave like
-regularly varying or
-rapidly varying or
-regularly bounded functions (that is, the functions
, for which a special limit behavior of
as is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented.