AUTHORS: Irina Astashova

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ABSTRACT: 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 third- and forth-order equations an asymptotic classification of all solutions is presented. Some applications of the results obtained are proposed

KEYWORDS: Qualitative properties, asymptotic behavior, nonlinear equations, blow-up, oscillatory solutions

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[23] I. Astashova, Positive solutions with nonpower asymptotic behavior and quasiperiodic solutions to an Emden–Fowler type higher order equations, Journal of Mathematical Sciences. 2015. 208, 1. P. 8–23.

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