Existence of solutions to resonant elliptic boundary value problems with unbounded discontinuous nonlinearities

We consider the situation when a resonant elliptic boundary value problem with an unbounded discontinuous nonlinearity is an idealization of a distributed system with continuous nonlinearities with respect to the phase variable and possessing narrow regions in the phase variable domain where the changes of nonlinear parameters are intractable. We study the existence of solutions to problems of this type.