Elliptic boundary-value problems with discontinuous nonlinearities

For a class of elliptic boundary value problems with discontinuous nonlinearities, the existence of strong solutions is established. Two applications are then developed. In particular, one of them is devoted to implicit elliptic equations of the form (–u)=(u), where is a continuous function and has a set of discontinuity points of Lebesgue measure zero. The abstract framework where these problems are studied is that of set-valued analysis.