Geodesic
Oscillation of second-order nonlinear differential equations with a damping term
Electronic journal of differential equations, Tome 2005 (2005)
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 $xg(x)$ for all $x\neq 0, r(t)$ for $t\geq t_{0}$. 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.
Classification : 34K15, 34C10
Keywords: oscillation, second order nonlinear differential equation, damping term 
@article{EJDE_2005__2005__a70,
     author = {Elabbasy,  Elmetwally M. and Hassan,  Taher S. and Saker,  Samir.H.},
     title = {Oscillation of second-order nonlinear differential equations with a damping term},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1075.34029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a70/}
}
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Elabbasy,  Elmetwally M.; Hassan,  Taher S.; Saker,  Samir.H. Oscillation of second-order nonlinear differential equations with a damping term. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a70/