Electron. J. Diff. Eqns., Vol. 2007(2007), No. 22, pp. 1-5.

On asymptotic behaviour of oscillatory solutions for fourth order differential equations

Seshadev Padhi, Chuanxi Qian

Abstract:
We establish sufficient conditions for the linear differential equations of fourth order
$$ (r(t)y'''(t))' =a(t)y(t)+b(t)y'(t)+c(t)y''(t)+f(t) $$
so that all oscillatory solutions of the equation satisfy
$$ \lim_{t\to\infty}y(t)=\lim_{t\to\infty}y'(t)=\lim_{t\to\infty}y''(t)= \lim_{t\to\infty}r(t)y'''(t)=0, $$
where $r:[0,\infty)\to(0,\infty),a,b,c$ and $f:[0,\infty)\to R$ are continuous functions. A suitable Green's function and its estimates are used in this paper.

Submitted December 2, 2006. Published February 4, 2007.
Math Subject Classifications: 34C10.
Key Words: Oscillatory solution; asymptotic behaviour.

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

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