We establish the existence of an entire weak solution for a class of stationary Schrödinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow-up at infinity. The proof relies on Chang's version of the Mountain Pass Lemma for locally Lipschitz functionals. Our result generalizes in a nonsmooth framework, a result of Rabinowitz  related to entire solutions of the Schrödinger equation.
"Variational Methods in the Study of Inequality Problems for Nonlinear Elliptic Systems with Lack of Compactness." Real Anal. Exchange 33 (1) 1 - 14, 2007/2008.