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Math Help - Prove that y goes to negative infinity

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    Prove that y goes to negative infinity

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

    Let x(t)>0 be a continuous solution to the equation

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

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

    and let y=x+h_2.

    Show that if y^{(3)}\leq 0 for arbitrarily large t then y\to-\infty as t\to\infty.
    It is easy to deduce the following results:

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

    (2) y^{(4)}<0

    (3) y>h_2

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

    Maybe these are useful, maybe not.

    Any help would be much appreciated. Thanks!
    Last edited by hatsoff; June 11th 2011 at 09:01 AM.
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