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

Dinu, Teodora-Liliana

doi:https://doi.org/10.1155/IJMMS/2006/73619

International Journal of Mathematics and Mathematical Sciences

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Volume 2006 | Article ID 073619 | https://doi.org/10.1155/IJMMS/2006/73619

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

Teodora-Liliana Dinu¹

Received05 Jul 2005

Revised14 Apr 2006

Accepted05 Jul 2006

Published17 Aug 2006

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.

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Copyright

Copyright © 2006 Hindawi Publishing Corporation. 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.

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