International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Issue 12, Article ID 73619, 13 pages
doi:10.1155/IJMMS/2006/73619

Standing wave solutions of Schrödinger systems with discontinuous nonlinearity in anisotropic media

Abstract

We establish the existence of an entire solution for a class of stationary Schrödinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow up at infinity. The proof is based on the critical point theory in the sense of Clarke and we apply Chang's version of the mountain pass lemma for locally Lipschitz functionals. Our result generalizes in a nonsmooth framework a result of Rabinowitz (1992) related to entire solutions of the Schrödinger equation.