Sturm-Liouville equations involving discontinuous nonlinearities

This paper deals with equations of Sturm-Liouville-type having nonlinearities on the righthand side being possibly discontinuous. We present different existence results of such equations under various hypotheses on the nonlinearities. Our approach relies on critical point theory for locally Lipschitz functionals. In particular, under suitable assumptions, an existence result of a non-zero local minimum for locally Lipschitz functionals is established.