IJPAM: Volume 38, No. 3 (2007)

BOUNDEDNESS AND STABILITY PROPERTIES OF
SOLUTIONS TO CERTAIN THIRD ORDER NONLINEAR
NON-AUTONOMOUS DIFFERENTIAL EQUATIONS

B.S. Ogundare
Department of Mathematics
Obafemi Awolowo University
Ile-Ife, NIGERIA
e-mails: ogundareb@yahoo.com, bogunda@oauife.edu.ng


Abstract.In this paper we give criteria for the boundedness and global asymptotic stability of solutions to certain third order nonlinear non-autonomous differential equation

\begin{displaymath}\stackrel{...}x+a(t)f(x,\dot{x})\ddot{x}+b(t)g(\dot{x})+c(t)h(x)=p(t;x,\dot{x},\ddot{x})\end{displaymath}

when $p\equiv 0$ and when $p\neq 0$, with the use of a single complete Lyapunov function.

The results here include and improve some well known results in the literature.

Received: March 23, 2007

AMS Subject Classification: 34D20, 34D99

Key Words and Phrases: boundedness, global asymptotic stability, Lyapunov function, third order nonlinear non-autonomous differential equations.

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 38
Issue: 3