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

Existence of weak solutions to some stationary Schr\"odinger equations with singular nonlinearity