A global approach to the Schrödinger-Poisson system: An Existence result in the case of infinitely many states

2013/02/11 by Otared Kavian, Kavian, Otared, Stéphane Mischler +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.1302.2588

openalex publication_date 2013/02/11 · arxiv created 2015/03/05 · arxiv updated 2015/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove the existence of a solution to a nonlinear Schrödinger--Poisson eigenvalue problem in dimension less than 3. Our proof is based on a global approach to the determination of eigenvalues and eigenfunctions which allows us to characterize the complete sequence of eigenvalues and eigenfunctions at once, via a variational approach, and thus differs from the usual and less general proofs developed for similar problems in the literature. Our approach seems to be new for the determination of the spectrum and eigenfunctions for compact and self-adjoint operators, even in a finite dimensional setting.

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