Hi guys. I've got what *should* be a simple problem, but it's giving me trouble. Here it is:

It is easy to deduce the following results:Let $\displaystyle x(t)>0$ be a continuous solution to the equation

$\displaystyle x^{(4)}(t)+q(t)f(x(t))=-h_2^{(4)}(t)$,

where $\displaystyle q>0$ and $\displaystyle xf(x)>0$ for $\displaystyle x\neq 0$, with $\displaystyle q,f,h_2$ continuous.

and let $\displaystyle y=x+h_2$.

Show that if $\displaystyle y^{(3)}\leq 0$ for arbitrarily large $\displaystyle t$ then $\displaystyle y\to-\infty$ as $\displaystyle t\to\infty$.

(1) $\displaystyle y^{(4)}+qf(y-h_2)=0$

(2) $\displaystyle y^{(4)}<0$

(3) $\displaystyle y>h_2$

(4) $\displaystyle y^{(3)}$ is strictly decreasing.

Maybe these are useful, maybe not.

Any help would be much appreciated. Thanks!