Singular solutions of nonlinear Schrödinger problem in bounded piecewise Dini-smooth Jordan domain

We prove the existence of positive singular solutions of the nonlinear equationΔu−μu=f(.,u)on Ω∖{0}, where Ω is a bounded simply connected piecewise Dini-smooth Jordan domain in R2, μ and f are, respectively, a signed measure on Ω and a Borel measurable function, required to satisfy suitable assumptions related to a new functional class J.