Complete asymptotic analysis of positive solutions of odd-order nonlinear differential equation

We study the asymptotic behavior of solutions of the odd-order differential equation of Emden-Fowler type x((2n+1))(t) = q(t)vertical bar x(t)vertical bar(gamma) sgn x(t) in the framework of regular variation under the assumptions that 0 < gamma < 1 and q(t) : [a, infinity) -> (0, infinity) is regularly varying function. We show that complete and accurate information can be acquired about the existence of all possible positive solutions and their asymptotic behavior at infinity.