Electron. J. Diff. Equ., Vol. 2010(2010), No. 23, pp. 1-10.

Oscillation of solutions for odd-order neutral functional differential equations

Tuncay Candan

Abstract:
In this article, we establish oscillation criteria for all solutions to the neutral differential equations
$$ [x(t)\pm ax(t\pm h)\pm bx(t\pm g)]^{(n)} =p\int_{c}^{d}x(t-\xi)d\xi+q\int_{c}^{d}x(t+\xi)d\xi, $$
where $n$ is odd, $h$, $g$, $a$ and $b$ are nonnegative constants. We consider 10 of the 16 possible combinations of +/- signs, and give some examples to illustrate our results.

Submitted December 9, 2009. Published February 4, 2010.
Math Subject Classifications: 34K11, 34K40.
Key Words: Neutral differential equations; oscillation of solutions; distributed deviating arguments.

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Tuncay Candan
Department of Mathematics, Faculty of Art and Science
Nigde University, Nigde, 51200, Turkey
email: tcandan@nigde.edu.tr

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