Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 22, pp. 1-5.

Title: On asymptotic behaviour of oscillatory solutions for 
      fourth order differential equations

Authors: Seshadev Padhi (Birla Inst. of Technology, Mesra, India)
         Chuanxi Qian   (Mississippi State Univ., MS, USA)

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.