In this work it is studied the higher order nonlinear equation
$\u^{( n)} (x)=f(x,u(x),u^{'}(x),\ldots ,u^{( n-1)} (x)) $
with $n\in \mathbb{N}$ such that $n\geq 2,$ $f:[ a,b]
\times \mathbb{R}^{n}\rightarrow \mathbb{R}$ a continuous
function, and the
two-point boundary conditions
$u^{(i)}(a) =A_{i},\text{ \ \ }A_{i}\in \mathbb{R},\text{ \
}i=0,\ldots
,n-3$,
$u^{( n-1) }(a) =u^{( n-1) }(b)=0.$
From one-sided Nagumo-type condition, allowing that $f$ can be
unbounded, it is obtained an existence and location result, that
is, besides the existence, given by Leray-Schauder topological
degree, some bounds on the solution and its derivatives till order
$(n-2)$ are given by well ordered lower and upper solutions.
An application to a continuous model of human-spine, via beam
theory, will be presented.
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