A uniqueness result for a Schrödinger-Poisson system with strong singularity

Yu, Shengbin and Chen, Jianqing: A uniqueness result for a Schrödinger-Poisson system with strong singularity. Electronic journal of qualitative theory of differential equations 87. pp. 1-15. (2019)

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Abstract

In this paper, we consider the following Schrödinger–Poisson system with strong singularity −∆u + φu = f(x)u , x ∈ Ω, −∆φ = u 2 , x ∈ Ω, u > 0, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where Ω ⊂ R3 is a smooth bounded domain, γ > 1, f ∈ L 1 (Ω) is a positive function (i.e. f(x) > 0 a.e. in Ω). A necessary and sufficient condition on the existence and uniqueness of positive weak solution of the system is obtained. The results supplement the main conclusions in recent literature.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 87
Page Range: pp. 1-15
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.87
Uncontrolled Keywords: Schrödinger-Poisson rendszer
Additional Information: Bibliogr.: p. 13-15. ; összefoglalás angol nyelven
Date Deposited: 2020. Jan. 27. 13:27
Last Modified: 2020. Jan. 27. 13:27
URI: http://acta.bibl.u-szeged.hu/id/eprint/64731

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