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.