Infinitely many solutions for a Schrodinger equation with sign-changing potential and nonlinear term

2019/03/07 by Long-Jiang Gu, Gu, Long-Jiang, Huan‐Song Zhou +1
Mathematics · #35J20 #35J61 #58E05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1903.03012

openalex publication_date 2019/03/07 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28

Abstract

We propose a new variational approach to finding multiple critical points for strongly indefinite problems without assuming the weak upper semicontinuity on the variational functionals. By this approach, we obtain the existence of infinitely many geometrically distinct solutions for a stationary periodic Schrödinger equation, in which the linear part is strongly indefinite and the nonlinear term is allowed to change sign in general ways.

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