  We deal with the existence of positive solutions for a two-point boundary
value problem associated with the nonlinear second order equation
$u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change its sign. We assume
that the function $g\colon\mathopen{[}0,+\infty\mathclose{[}\to\mathbb{R}$ is
continuous, $g(0)=0$ and satisfies suitable growth conditions, so as the case
$g(s)=s^{p}$, with $p>1$, is covered. In particular we suppose that $g(s)/s$ is
large near infinity, but we do not require that $g(s)$ is non-negative in a
neighborhood of zero. Using a topological approach based on the Leray-Schauder
degree we obtain a result of existence of at least a positive solution that
improves previous existence theorems.
