International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 73619, 13 pages
Standing wave solutions of Schrödinger systems with
discontinuous nonlinearity in anisotropic media
Department of Mathematics, “Fraţii Buzeşti” College, Boulevard Ştirbei-Vodă no. 5, Craiova 200352, Romania
Received 5 July 2005; Revised 14 April 2006; Accepted 5 July 2006
Copyright © 2006 Teodora-Liliana Dinu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.