Precise asymptotic behavior of solutions of the sublinear Emden-Fowler differential equation

The aim of this paper is to show that if the sublinear Emden-Fowler differential equation x ''(t) + q(t)vertical bar x(t)vertical bar(gamma) sgnx(t) = 0, 0 < gamma < 1, (A) with regularly varying coefficient q(t) is studied in the framework of regular variation, not only necessary and sufficient conditions for the existence of nontrivial regularly varying solutions of (A) can be established, but also precise information can be acquired about the asymptotic behavior at infinity of these solutions. (C) 2010 Elsevier Inc. All rights reserved.