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| For the equation
$y^{(n)}+p(x,y,y',...y^{(n-1)})\;|y|^k {\rm sgn} y = 0$
with $n\ge1,$ real $k>1$ and a continuous function $p$ some results about the asymptotic behavior of blow-up and Kneser solutions are obtained. The existence of such solutions with non-power asymptotic behavior is proved for constant negative $p$ and $n=12,13,14.$
It is also proved that the equation can have an oscillatory solution with special asymptotic behavior. This yields the existence of
solutions with arbitrary number of zeros.
The problem of asymptotic equivalence of solutions is investigated for the above equation and a slightly modified one. |
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