Geodesic
Convergence of solutions of certain non-homogeneous third order ordinary differential equations
Kragujevac Journal of Mathematics, Tome 31 (2008), p. 5

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Zbl
This paper is concerned with differential equations of the form $\st{...}{x}+a\ddot{x}+g(\dot{x})+h(x)=p(t,x,\dot{x},\ddot{x})$ where $a$ is a positive constant and $g$,$h$ and $p$ are continuous in their respective arguments, with functions $g$ and $h$ not necessarily differentiable. By introducing a complete Lyapunov function, as well as restricting the incrementary ratio $\eta^{-1}\{h(\xi + \eta)-h(\xi)\},(\eta \neq 0),$ 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.
Classification : 34D40 34D20 34C25
Keywords: convergence, Lyapunov functions, nonlinear third-order equation 
A. U. Afuwape; M.O. Omeike. Convergence of solutions of certain non-homogeneous third order ordinary differential equations. Kragujevac Journal of Mathematics, Tome 31 (2008), p. 5 . http://geodesic.mathdoc.fr/item/KJM_2008_31_a0/
@article{KJM_2008_31_a0,
     author = {A. U. Afuwape and M.O. Omeike},
     title = {Convergence of solutions of certain non-homogeneous third order ordinary differential equations},
     journal = {Kragujevac Journal of Mathematics},
     pages = {5 },
     year = {2008},
     volume = {31},
     zbl = {1199.34246},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2008_31_a0/}
}
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