Omeike, Mathew New results on the asymptotic behavior of a third-order nonlinear differential equation. (English) Zbl 1198.34085 Differ. Equ. Appl. 2, No. 1, 39-51 (2010). The author studies the equation \[ x'''+g(x,x')x''+f(x,x') = p(t) , \] where \(g,f,g_{x},f_{x}\in C({\mathbb R}\times {\mathbb R},{\mathbb R})\) and \(p\in C([0,\infty ),{\mathbb R})\). It is assumed that the solutions \(x(t)\) of the considered equation exist and are unique. Sufficient conditions are established such that for all solutions there holds: (a) There exists a constant \(D>0\) such that \(|x^{(i)}(t)|\leq D\), for sufficiently large \(t\). (b) \(x^{(i)}(t)\rightarrow 0\), as \(t\rightarrow \infty \); \(i=0,1,2\). Reviewer: Vojislav Marić (Novi Sad) Cited in 5 Documents MSC: 34D05 Asymptotic properties of solutions to ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations Keywords:3-rd order nonlinear differential equation; boundedness; asymptotic behavior PDFBibTeX XMLCite \textit{M. Omeike}, Differ. Equ. Appl. 2, No. 1, 39--51 (2010; Zbl 1198.34085) Full Text: DOI Link