Electron. J. Diff. Eqns., Vol. 2005(2005), No. 76, pp. 1-13.

Oscillation of second-order nonlinear differential equations with a damping term

Elmetwally M. Elabbasy, Taher S. Hassan, Samir. H. Saker

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 $xg(x)$ greater than 0 for all $x\neq 0$, $r(t)$ greater than 0 for $t\geq t_{0}$ greater than 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.

Acorrigendum was posted on January 2, 2008. A new assumption is included in Theorems 2.2 and 2.4, and Example 2.3 is modified. Please see the last page of this manuscript.

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Elmetwally M. Elabbasy
Department of Mathematics
Faculty of Science, Mansoura University
Mansoura, 35516, Egypt
email: emelabbasy@mans.edu.eg
Taher S. Hassan
Department of Mathematics
Faculty of Science, Mansoura University
Mansoura, 35516, Egypt
email: tshassan@mans.edu.eg
Samir H. Saker
Department of Mathematics
Faculty of Science, Mansoura University
Mansoura, 35516, Egypt
email: shsaker@mans.edu.eg

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