Teodora-Liliana Dinu

Ground State Solutions of Nonlinear Stationary Schrödinger Systems with Discontinuous Nonlinearity and Variable Potential

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 the Mountain Pass Lemma for locally Lipschitz functionals. Our result generalizes in a nonsmooth framework a result of Rabinowitz (1992) on the existence of entire solutions of the nonlinear Schrödinger equation.

Keywords:
Obstruction, homotopy, cohomology, cochain operation, $k$-invariant.

MSC 2000: 55Q25, 55S20, 55S35, 55S37, 55S45