  We prove some existence (and sometimes also uniqueness) of weak solutions to
some stationary equations associated to the complex Schr\''{o}dinger operator
under the presence of a singular nonlinear term. Among other new facts, with
respect some previous results in the literature for such type of nonlinear
potential terms, we include the case in which the spatial domain is possibly
unbounded (something which is connected with some previous localization results
by the authors), the presence of possible non-local terms at the equation, the
case of boundary conditions different to the Dirichlet ones and, finally, the
proof of the existence of solutions when the right-hand side term of the
equation is beyond the usual $L^2$-space.
