Commun. Korean Math. Soc. 2004; 19(2): 307-319
Printed June 1, 2004
Copyright © The Korean Mathematical Society.
Ravi P. Agarwal, S. R. Grace, S. Dontha
Florida Institute of Technology, Cairo University, Florida Institute of Technology
In this paper, we establish some new oscillation criteria for the functional differential equations of the form $$ \begin{array}{l} \displaystyle \frac{d}{dt}\left( \frac{1}{a_{n-1}(t)}\frac{d}{dt}\left(\frac{1}{a_{n-2}(t)}\frac{d}{dt}\left( \cdots \left( \frac{1}{a_1(t)}\frac{d}{dt}x(t)\right) \cdots \right) \right) \right)^{\alpha} \\ \displaystyle + \delta \left[ f_1\left(t,x[g_1(t)],\frac{d}{dt}x[h_1(t)]\right) +f_2\left(t,x[g_2(t)], \frac{d}{dt}x[h_2(t)]\right)\right] {\hskip-0.13cm}={\hskip-0.06cm}0 \dd \end{array}$$ via comparing it with some other functional differential equations whose oscillatory behavior is known.
Keywords: oscillation, comparison, functional differential equations
MSC numbers: 34C10, 34C15
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