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 → ∞.