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

Abstract

In this paper, we consider two different models of nonlinear ordinary differential equations (ODEs) of second order. We construct two new Lyapunov functions to investigate boundedness of solutions of those nonlinear ODEs of second order. By using the Lyapunov direct or second method and inequality techniques, we prove two new theorems on the boundedness solutions of those ODEs of second order as t → ∞. When we compare the conditions of the theorems of this paper with those of Meng in (

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

“…Moreover, taking f (t; x; x 0 ) = p(t)g(x 0 ) and (x) = x or '(x) = x in Eq. (1), Theorem 1 or Theorem 2 in [15] is gotten, respectively. So, Eq.…”

“…In this paper, motivated by the work of Tunc and Mohammed [15], we deal with the following second order nonlinear di¤erential equation:…”