Asymptotic representations of solutions of nonautonomous ordinary differential equations with regularly varying nonlinearities

Extremal solutions to a system of n nonlinear differential equations and regularly varying functions

“…As an application, they examined Equations and . Results of a similar character can be found in by Evtukhov and Samoilenko, who considered the equation , where F is a regularly varying function of index different from 1 and p is a continuous function. They made a classification of positive solutions of whose behavior is related to regularly varying and rapidly varying functions.…”

Asymptotic behavior of increasing solutions to a system of nonlinear differential equations

“…Further, the theory of regular variation was applied to the study of odd-order equations of the form (21) with σ = 1 in [14], and of nth-order equations of the form y (n) + σ p(t)F (y) = 0 with a regularly varying (at 0 or ∞) nonlinearity F of an index different from one in [15]; see also comments on the paper [15] presented in [14], which clarify the setting and describe a comparison with the results in a ''standard'' form.…”

Asymptotic behavior of solutions of a nonlinear ordinary differential equation of order n

“…Lemmas 1-4 were proved in [10]. Lemma 5 follows directly from Lemmas 1-4 and the relation for determination of the kth derivative .k 2/ in the form of the fraction of two functions (see [11, p. 49], Chap.…”