Electron. J. Diff. Eqns., Vol. 2005(2005), No. 65, pp. 1-14.

Asymptotic behaviour of solutions to $n$-order functional differential equations

Seshadev Padhi

Abstract:
We establish conditions for the linear differential equation
$$ y^{(n)}(t)+p(t)y(g(t))=0 $$
to have property A. Explicit sufficient conditions for the oscillation of the the equation is obtained while dealing with the property A of the equations. A comparison theorem is obtained for the oscillation of the equation with the oscillation of a third order ordinary differential equation.

Submitted September 4, 2004. Published June 23, 2005.
Math Subject Classifications: 34C10, 34K15.
Key Words: Oscillatory solution; nonoscillatory solution; property A.

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Seshadev Padhi
Department of Applied Mathematics
Birla Institute of Technology, Mesra, Ranchi -835 215, India
and Department of Mathematics and Statistics
Mississippi State University
MS-39762, Mississippi State, USA
email: ses_2312@yahoo.co.in

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