Electron. J. Diff. Eqns., Vol. 2006(2006), No. 35, pp. 1-10.

Stability and boundedness of solutions to certain fourth-order differential equations

Cemil Tunc

Abstract:
We give criteria for the asymptotic stability and boundedness of solutions to the nonlinear fourth-order ordinary differential equation
$$ x^{(4)}+\varphi (\ddot{x})\dddot{x}+f(x,\dot{x}) \ddot{x}+g(\dot{x})+h(x)=p(t,x,\dot{x},\ddot{x},\dddot{x})\,, $$
when $p\equiv 0$ and when $p\neq 0$. Our results include and improve some well-known results in the literature.

Submitted November 17, 2005. Published March 21,2006.
Math Subject Classifications: 34D20, 34D99.
Key Words: Fourth order differential equations; stability; boundedness

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Cemil Tunç
Department of Mathematics
Faculty of Arts and Sciences
Yüzüuncü Yil University, 65080, Van, Turkey
email: cemtunc@yahoo.com

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