Convergence of solutions of certain non-homogeneous third order ordinary differential equations. (English) Zbl 1199.34246

Afuwape, A. U.; Omeike, M. O.

Kragujevac J. Math. 31, 5-16 (2008).

Authors’ abstract: This paper is concerned with differential equations of the form \[ \dddot x+a\ddot x+g(\dot x)+h(x)=p(t,x,\dot x,\ddot x), \] where \(a\) is a positive constant and \(g\), \(h\) and \(p\) are continuous in their arguments. By introducing a complete Lyapunov function, as well as restricting the incrementary ratio \(\eta^{-1}\{h(\xi+\eta)-h(\xi)\}\), (\(\eta\neq0\)), of \(h\) to a closed sub-interval of the Routh-Hurwitz interval, we prove the convergence of solutions for this equation. This generalizes earlier results.

Reviewer: Vojislav Marić (Novi Sad)

MSC:

34D05	Asymptotic properties of solutions to ordinary differential equations
34A34	Nonlinear ordinary differential equations and systems

Keywords:

complete Lyapunov functions; Routh-Hurwitz interval