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Abstract
In this paper, given $f : I \times (C(I))^2 \times \mathbb{R}^2 \leftarrow \mathbb{R}$ a $L^1$ Carathéodory
function, it is considered the functional fourth order equation
$u^(iv) (x) = f(x, u, u', u'' (x), u''' (x))$
together with the nonlinear functional boundary conditions
$L_0(u, u', u'', u (a)) = 0 = L_1(u, u', u'', u' (a))$
$L_2(u, u', u'', u'' (a), u''' (a)) = 0 = L_3(u, u', u'', u'' (b}, u''' (b)):$
Here $L_i, i$ = 0; 1; 2; 3, are continuous functions satisfying some adequate
monotonicity assumptions.
It will be proved an existence and location result in presence of non ordered
lower and upper solutions and without monotone assumptions on the right
hand side of the equation.
Mathematics Subject Classification: Primary: 34B15, 34K10; Secondary: 34B10, 34K45.
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