Asymptotic analysis of positive solutions of a class of third order nonlinear differential equations in the framework of regular variation

This paper is devoted to the asymptotic analysis of the third order sublinear differential equation\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty} $$ x^{\prime \prime \prime } + q(t)|x|^{\gamma }\textrm {sgn}\;x = 0, \quad q(t) > 0, \quad 0 < \gamma < 1, \qquad \mathrm{(\textrm {A})} $$ \end{document} in the framework of regular variation. It is shown that in case q ( t ) is nearly regularly varying accurate information can be acquired about the existence of possible positive solutions of (A) and their asymptotic behavior as t → ∞.