  Pathwise non-uniqueness is established for non-negative solutions of the
parabolic stochastic pde $$\frac{\partial X}{\partial
t}=\frac{\Delta}{2}X+X^p\dot W+\psi,\ X_0\equiv 0$$ where $\dot W$ is a white
noise, $\psi\ge 0$ is smooth, compactly supported and non-trivial, and
$0<p<1/2$. We further show that any solution spends positive time at the 0
function.
