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

Interaction of zero-mass meson and charged dust in axially symmetric fields

1972 ◽  
Vol 71 (1) ◽  
pp. 293-300 ◽  
Author(s):  
R.M. Misra ◽  
Deo Bhushan Pandey
Keyword(s):  
Charged Dust ◽  
Axially Symmetric ◽  
Zero Mass

scholarly journals Some axially symmetric zero mass meson solutions of Einstein's equations

1975 ◽  
Vol 19 (2) ◽  
pp. 140-145 ◽  
Author(s):  
L. K. Patel ◽  
V. M. Trivedi
Keyword(s):  
Exact Solutions ◽  
Electromagnetic Fields ◽  
Axially Symmetric ◽  
Einstein’S Equations ◽  
Field Equations ◽  
Einstein's Equations ◽  
Zero Mass ◽  
Oblate Spheroidal

AbstractAn axially symmetric metric in oblate spheroidal co-ordinates is considered. Two exact solutions of the field equations corresponding to zero mass meson fields are obtained. The details of the solutions are also discussed. These solutions are also generalized to include electromagnetic fields.

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 Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system

2021 ◽  
Vol 6 (7) ◽  
pp. 7833-7844
Author(s):  
Qiongfen Zhang ◽  
◽  
Kai Chen ◽  
Shuqin Liu ◽  
Jinmei Fan ◽  
...  
Keyword(s):  
Poisson System ◽  
Axially Symmetric
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