A uniqueness result for a Schrödinger-Poisson system with strong singularity
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...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Schrödinger-Poisson rendszer |
| doi: | 10.14232/ejqtde.2019.1.87 |
| Online Access: | http://acta.bibl.u-szeged.hu/64731 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 1-15 |
| ISSN: | 1417-3875 |