Metodi variazionali nello studio di problemi al contorno con parte non lineare discontinua

The main purpose of this paper is to use variational methods in the study of problems of following type: {Mathematical expression} Here Ω is supposed to be a bounded domain with smooth boundary ∂ Ω, L an elliptic operator, λ∈IR and f(x, t) a real function defined on {Mathematical expression} having one or several simple discontinuities on t. Mainly we are interested in solutions which satisfy (.) a. e., which are most meaningful in physical problems, and we prove various existence theorems for several choices of L, f and λ. The main difficulty consists in the fact that the functionals related to (.) are not Fréchet differentiable in every point, since f is discontinuous