  We study boundary value problems associated with singular, strongly nonlinear
differential equations with functional terms of type
$$\big(\Phi(k(t)\,x'(t))\big)' + f(t,\mathcal{G}_x(t))\,\rho(t, x'(t)) = 0$$ on
a compact interval $[a,b]$. These equations are quite general due to the
presence of a strictly increasing homeomorphism $\Phi$, the so-called
$\Phi$-Laplacian operator, of a nonnegative function $k$, which may vanish on a
set of null measure, and moreover of a functional term $\mathcal{G}_x$. We look
for solutions, in a suitable weak sense, which belong to the Sobolev space
$W^{1,1}([a,b])$. Under the assumptions of the existence of a well-ordered pair
of upper and lower solutions and of a suitable Nagumo-type growth condition, we
prove an existence result by means of fixed point arguments.
