Entire solutions of Schrödinger elliptic systems with discontinuous nonlinearity and sign-changing potential

2005/11/08 by Teodora Liliana Dinu, Dinu, Teodora Liliana
Computer Science · Mathematics · Physics and Astronomy · #35J50 #49J52 #58E05 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #math-ph #math.AP #math.MP #msc:35J50 #msc:49J52 #msc:58E05

paper · pdf · doi:10.48550/arxiv.math/0511192

12 pages

arxiv created 2005/11/08 · openalex publication_date 2005/11/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citerabi related to entire solutions of the Schrödinger equation.

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