Opuscula Mathematica
Opuscula Math. 32, no. 4 (), 719-730
http://dx.doi.org/10.7494/OpMath.2012.32.4.719
Opuscula Mathematica

Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments




Abstract. Oscillation criteria are established for second order nonlinear neutral differential equations with deviating arguments of the form \[r(t)\psi(x(t))|z'(t)|^{\alpha -1} z'(t)+ \int_a^b q(t,\xi)f(x(g(t,\phi)))d\sigma (\xi) =0,\quad t\gt t_0,\] where \(\alpha \gt 0\) and \(z(t)= x(t)+p(t)x(t-\tau)\). Our results improve and extend some known results in the literature. Some illustrating examples are also provided to show the importance of our results.
Keywords: oscillation, second order, neutral differential equations, deviating arguments.
Mathematics Subject Classification: 34C10, 34C15.
Cite this article as:
Elmetwally M. Elabbasy, T. S. Hassan, O. Moaaz, Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments, Opuscula Math. 32, no. 4 (2012), 719-730, http://dx.doi.org/10.7494/OpMath.2012.32.4.719
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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