Asymptotic properties of solutions of the equationy′'=f(x)ϕ(y)

On the Asymptotics of Solutions of Nonlinear Second-Order Differential Equations

“…(1.1) decaying at infinity were obtained in [8,9] for the case in which ϕ(y) is different from |y| σ+1 sgn y and in a sense close to functions of the form (1.4). For any solution y(t) of this kind, two-sided asymptotic estimates for the ratio y(t)/ϕ(y(t)) as t → +∞ were also obtained.…”

On a class of functional differential equations having slowly varying solutions

“…Linear equations were first studied by Omey in 1981, [13]. Systematic investigations in this direction started with a paper of Marić and Tomić [11] published in 1976. A complete survey of the results on differential equations, both linear and nonlinear, developed by means of regular variation is given in the monograph of Marić [10].…”

An Asymptotic Analysis of Solutions of a Second Order Nonlinear Differential Equation

“…Such study of asymptotics of solutions of di¤erential equations via regular variation was initiated in the seminal paper of V. G. Avakumović [1] and about 30 years later extended and developed in [24]. Then, after the monograph [23] appeared, numerous papers in that spirit have been published, dealing also with some more general di¤erential equation of the second order, the ones of higher orders and some systems, functional di¤erential equations, di¤erence and dynamic ones and also some partial di¤erential ones (see e.g.…”

“…Then, after the monograph [23] appeared, numerous papers in that spirit have been published, dealing also with some more general di¤erential equation of the second order, the ones of higher orders and some systems, functional di¤erential equations, di¤erence and dynamic ones and also some partial di¤erential ones (see e.g. [7]- [22], [24]- [32], [34]- [35]). In [5] V. M. Evtukhov and A. M. Samoilenko by a di¤erent approach studied the n-th order equation x ðnÞ ¼ a 0 gðtÞfðxÞ for both…”