scholarly journals On the planar Schrödinger–Poisson system with zero mass potential

2021 ◽  
Author(s):  
Fangfang Liao ◽  
Xiaoping Wang
Keyword(s):  
Poisson System ◽  
Zero Mass

Axially symmetric solutions of the Schrödinger–Poisson system with zero mass potential in R2

2020 ◽  
Vol 104 ◽  
pp. 106244 ◽  
Author(s):  
Lixi Wen ◽  
Sitong Chen ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Poisson System ◽  
Axially Symmetric ◽  
Zero Mass

scholarly journals On the planar Schrödinger-Poisson system with zero mass potential

2021 ◽  
Author(s):  
Fangfang Liao ◽  
Xiaoping Wang
Keyword(s):  
Symmetric Solution ◽  
Poisson System ◽  
Radially Symmetric Solution ◽  
Zero Mass ◽  
Analytical Approaches

In this paper, we prove that the following planar Schrödinger-Poisson system with zero mass -Δu+φu=f(u), x∈R^2, Δφ= 2πu^2, x∈R^2, admits a nontrivial radially symmetric solution under weaker assumptions on f by using some new analytical approaches.

Schrödinger–Poisson system with zero mass and convolution nonlinearity in R 2

2021 ◽  
pp. 1-21
Author(s):  
Heng Yang
Keyword(s):  
Ground State ◽  
Exponential Growth ◽  
Riesz Potential ◽  
Poisson System ◽  
Nontrivial Solutions ◽  
Ground State Solutions ◽  
Zero Mass ◽  
Subcritical Exponential Growth ◽  
New Ideas ◽  
Mass Case

In this paper, we prove the existence of nontrivial solutions and ground state solutions for the following planar Schrödinger–Poisson system with zero mass − Δ u + ϕ u = ( I α ∗ F ( u ) ) f ( u ) , x ∈ R 2 , Δ ϕ = u 2 , x ∈ R 2 , where α ∈ ( 0 , 2 ), I α : R 2 → R is the Riesz potential, f ∈ C ( R , R ) is of subcritical exponential growth in the sense of Trudinger–Moser. In particular, some new ideas and analytic technique are used to overcome the double difficulties caused by the zero mass case and logarithmic convolution potential.

scholarly journals Observers of Vlasov-Poisson system

2020 ◽  
Vol 53 (2) ◽  
pp. 5946-5951
Author(s):  
Amadou Cisse ◽  
Mohamed Boutayeb
Keyword(s):  
Poisson System
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