On a semilinear parabolic equation

We introduce a general class of potentials $V=V(x,t)$ so that the semilinear parabolic equation $a\Delta u-\frac \partial{\partial t} u+ V u^p =0$ in $\mathbb{R}^n\times ]0,\infty[, n\geq 3,\, p>1$, $a>0$, has global positive continuous solutions. These results extend the recent ones proved by Zhang to a more general class of potentials.