Existence theorems for noncoercive elliptic problems with discontinuous nonlinearities Original Research Article

In this paper we are interested for elliptic problems of Ambrosetti–Prodi type with discontinuous nonlinearities. The differential operator is the p-Laplacian and we use a variational method for locally Lipschitz functionals due to Chang. We do not use the method of upper and lower solution and we do not suppose any monotonicity condition on the right-hand side.