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The asymptotic behavior of solutions of the odd-order differential equation of Emden-Fowler type x(t) + q(t)|x(t)|sgn x(t) = 0, is studied in the framework of regular variation, under the assumptions that 0 < γ < 1 and q(t) : [a,∞) → (0,∞) is regularly varying function. It is shown that complete and accurate information can be acquired about the existence of all possible positive solutions and their asymptotic behavior at infinity.

Asymptotic behavior of positive solutions of odd order Emden-Fowler type differential equations in the framework of regular variation