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.