Abstract
In this paper, we consider a second order nonlinear differential equation and establish two new theorems about the existence of the bounded solutions of a second order nonlinear differential equation. In these theorems, we use different Lyapunov functions with different conditions but we get the same result. In addition, two examples are given to support our results with some figures.
Highlights
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
As far as we know, it should be noted in the relevant literature that so far, the second method of Lyapunov is the most e¤ective tool for studying qualitative
The solution of Eq (13) with the initial conditions x(0) = 0; y(0) = 1 in t 2 [0; 10]: It is clear that the conditions (A1); (A2); (A4); (A5) and (A6) are satis...ed
Summary
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. C 2021 Ankara University C om munications Faculty of Sciences U niversity of A nkara-Series A 1 M athem atics and Statistics features of nonlinear higher order equations without getting solutions of the equations. This method needs the creation of an appropriate function or functionality that gives concrete results for the problem being studied.
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