On Asymptotic Classification of Solutions to Nonlinear Third- and Fourth-Order Differential Equations with Power Nonlinearity

The asymptotic behavior of all solutions to the fourth and the third order Emden -Fowler type differential equation is investigated. The author’s previously obtained results are supplemented. The equation of the n-th order is transformed into a system on the (n - 1)-dimensional sphere. By the investigation of asymptotic behavior to all possible trajectories of this system the asymptotic classification of all solutions to the equation is obtained.

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