Opuscula Math. 32, no. 4 (2012), 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

Elmetwally M. Elabbasy
T. S. Hassan
O. Moaaz

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.

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• Elmetwally M. Elabbasy
• Mansoura University, Department of Mathematics, Faculty of Science Mansoura, Egypt
• T. S. Hassan
• Mansoura University, Department of Mathematics, Faculty of Science Mansoura, Egypt
• O. Moaaz
• Mansoura University, Department of Mathematics, Faculty of Science Mansoura, Egypt
• Revised: 2012-02-08.
• Accepted: 2012-02-20.