Oscillation of Nonlinear Delay Differential Equation with Non-Monotone Arguments

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Özkan Öcalan
Nurten Kilic
Sermin Sahin
Umut Mutlu Ozkan

Abstract

Consider the first-order nonlinear retarded differential equation

$$

x^{\prime }(t)+p(t)f\left( x\left( \tau (t)\right) \right) =0, t\geq t_{0}

$$

where $p(t)$ and $\tau (t)$ are function of positive real numbers such that $%\tau (t)\leq t$ for$\ t\geq t_{0},\ $and$\ \lim_{t\rightarrow \infty }\tau(t)=\infty $. Under the assumption that the retarded argument is non-monotone, new oscillation results are given. An example illustrating the result is also given.

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References

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