We prove existence and uniqueness of solutions of a semilinear PDE driven by a Bessel type generator $L^\delta$ with low dimension $0 < \delta < 1$. $L^\delta$ is a local operator, whose drift is the derivative of $x \mapsto \log (\vert x\vert)$: in particular it is a Schwartz distribution, which is not the derivative of a continuous function. The solutions are intended in a duality ("weak") sense with respect to state space $L^2(\R_+, d\mu),$ $\mu$ being an invariant measure for the Bessel semigroup.