  We consider semilinear equation of the form $-Lu=f(x,u)+\mu$, where $L$ is
the operator corresponding to a transient symmetric regular Dirichlet form
${\mathcal E}$, $\mu$ is a diffuse measure with respect to the capacity
associated with ${\mathcal E}$, and the lower-order perturbing term $f(x,u)$
satisfies the sign condition in $u$ and some weak integrability condition (no
growth condition on $f(x,u)$ as a function of $u$ is imposed). We prove the
existence of a solution under mild additional assumptions on ${\mathcal E}$. We
also show that the solution is unique if $f$ is nonincreasing in $u$.
