  We consider one-dimensional stochastic heat equation with nonlinear drift,
$\displaystyle \partial_t u=\frac{1}{2}\Delta u+b(u)u+\sigma(u)\dot{W}(t,x)$,
where $b:\mathbb{R}_{+}\to \mathbb{R}$ is a continuous function and
$\sigma:\mathbb{R}_{+}\to \mathbb{R}$ is a continuous function with suitable
property. We will construct nonnegative solutions to such SPDEs.
