Entire solutions of Schrodinger elliptic systems with discontinuous nonlinearity and sign‐changing potential
Abstract
We establish the existence of an entire solution for a class of stationary Schrodinger 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 the result of Rabinowitz [16] on the existence of entire solutions of the nonlinear Schrödinger equation.
First Published Online: 14 Oct 2010
Keywords:
nonlinear elliptic systems, entire solution, Lipschitz functional, Clarke generalized gradientHow to Cite
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Copyright (c) 2006 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2006 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.