Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 76, pp. 1-13.
Title: Oscillation of second-order nonlinear differential equations
with a damping term
Authors: Elmetwally M. Elabbasy (Mansoura Univ., Egypt)
Taher S. Hassan (Mansoura Univ., Egypt)
Samir. H. Saker (Mansoura Univ., Egypt)
Abstract:
This paper concerns the oscillation of solutions to the differential equation
$$
(r(t) x'(t))'+ p(t) x'(t) + q(t) g( x(t) ) =0,
$$
where $xg(x)>0$ for all $x\neq 0$, $r(t)>0$ for
$t\geq t_{0}>0$. No sign conditions are imposed on $p(t)$ and $q(t)$.
Our results solve the open problem posed by Rogovchenko [27],
complement the results in Sun [29], and improve a number of existing
oscillation criteria. Our main results are illustrated with examples.
Submitted April 5, 2005. Published July 8, 2005.
Math Subject Classifications: 34K15, 34C10.
Key Words: Oscillation; second order nonlinear differential equation;
damping term.
A corrigendum posted on January 2,2008. A new assumption is included
in Theorems 2.2 and 24, and Example is modified. Please see the last
page of this manuscrpt.