Asymptotically linear solutions of differential equations via Lyapunov functions

Abstract

We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general results regarding Emden-Fowler like equations.

On the asymptotic analysis of bounded solutions to nonlinear differential equations of second order

“…Then we can say the same for all the solutions of ODE (16) and their first derivatives. We can observe the behaviors of the paths of ODE (16) by Figs. 1-4.…”

The existence of the bounded solutions of a second order nonhomogeneous nonlinear differential equation

“…For more than sixty years, a great deal of work has been done by various authors to investigate the autonomous and non-autonomous second order nonlinear ordinary di¤erential equations (ODEs) ( [1]- [5], [7]- [14], [16], [17], [19] ) and references cited therein.…”

Asymptotic properties of solutions to second-order difference equations

“…For second-order equations, asymptotically linear solutions are most often studied. Asymptotically linear solutions of differential equations are considered, for example, in papers [2,5,[10][11][12]14]. Asymptotically linear solutions of difference equations are studied, for example, in papers [1,3,4,13,15,16].…”