On the oscillation of certain functional differential equations
Commun. Korean Math. Soc. 2004 Vol. 19, No. 2, 307-319
Printed June 1, 2004
Ravi P. Agarwal, S. R. Grace, S. Dontha
Florida Institute of Technology, Cairo University, Florida Institute of Technology
Abstract : 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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