Entire solutions of Schrödinger elliptic systems with discontinuous nonlinearity and sign-changing potential
Teodora Liliana Dinu
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 rabi related to entire solutions of the Schrödinger equation.
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