On qualitative properties and asymptotic behavior of solutions to higher-order nonlinear differential equations
نویسنده
چکیده
We discuss the asymptotic behavior of solutions to a higher-order Emden–Fowler type equation with constant potential. Several author’s results are presented concerning both positive and oscillatory solutions to equations with regular and singular nonlinearities. We discuss the existence and asymptotic behavior of “blowup” solutions. Results on the asymptotic behavior of oscillating solutions are formulated. For the thirdand forth-order equations an asymptotic classification of all solutions is presented. Some applications of the results obtained are proposed. Key–Words: Qualitative properties, asymptotic behavior, nonlinear equations, blow-up, oscillatory solutions.
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