  In this paper, we focus our attention on the positive solutions to
second-order nonlinear ordinary differential equations of the form
$u''+q(t)g(u)=0$, where $q$ is a sign-changing weight and $g$ is a superlinear
function. We exploit the classical shooting approach and the comparison theorem
to present non-degeneracy and exact multiplicity results for positive
solutions. This completes the multiplicity results obtained by Feltrin and
Zanolin. Numerical examples and some related open problems are also discussed.
