On asymptotic classification of solutions to nonlinear regular and singular third- and fourth-order differential equations with power nonlinearity

Abstract

For the equation y(n)+ p0|y|ksign y = 0, in the cases n = 3; 4, p0> 0 or p0< 0 for regular nonlinearity k > 1 and singular nonlinearity 0 < k < 1 asymptotic classification of all solutions are given. It is the first time when all results on this classification are represented together for regular and singular cases.