Approximation of the resonance boundary-value problems of elliptic type with a discontinuous nonlinearity

We consider the situation in which a resonance elliptic boundary-value problem with a discontinuous nonlinearity is an idealization of a distributed system with nonlinearities continuous in the phase variable and having narrow areas in the domain of the phase variable in which the tracking of the change of nonlinear parameters is impossible. We study the question of proximity of the solution sets of the original and idealized systems.