scholarly journals Existence of ground state solutions for the planar axially symmetric Schrödinger-Poisson system

2017 ◽  
Vol 22 (11) ◽  
pp. 1-18 ◽  
Author(s):  
Sitong Chen ◽  
◽  
Xianhua Tang
Keyword(s):  
Ground State ◽  
Poisson System ◽  
Axially Symmetric ◽  
Ground State Solutions

scholarly journals Symmetry and concentration behavior of ground state in axially symmetric domains

2004 ◽  
Vol 2004 (12) ◽  
pp. 1019-1030
Author(s):  
Tsung-Fang Wu
Keyword(s):  
Ground State ◽  
Semilinear Elliptic Equation ◽  
Bounded Domains ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Axially Symmetric ◽  
Ground State Solutions ◽  
Semilinear Elliptic ◽  
Necessary And Sufficient ◽  
Concentration Behavior

We letΩ(r)be the axially symmetric bounded domains which satisfy some suitable conditions, then the ground-state solutions of the semilinear elliptic equation inΩ(r)are nonaxially symmetric and concentrative on one side. Furthermore, we prove the necessary and sufficient condition for the symmetry of ground-state solutions.

Existence and Concentration of Positive Ground State Solutions for Schrödinger-Poisson Systems

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Jun Wang ◽  
Lixin Tian ◽  
Junxiang Xu ◽  
Fubao Zhang
Keyword(s):  
Small Parameter ◽  
Ground State ◽  
Ground State Solution ◽  
Real Parameter ◽  
State Solution ◽  
Poisson System ◽  
Ground State Solutions ◽  
Subcritical Nonlinearity

AbstractIn this paper, we study the existence and concentration of positive ground state solutions for the semilinear Schrödinger-Poisson systemwhere ε > 0 is a small parameter and λ ≠ 0 is a real parameter, f is a continuous superlinear and subcritical nonlinearity. Suppose that b(x) has a maximum. We prove that the system has a positive ground state solution

Concentration behavior of ground state solutions for a fractional Schrödinger–Poisson system involving critical exponent

2019 ◽  
Vol 21 (06) ◽  
pp. 1850027 ◽  
Author(s):  
Zhipeng Yang ◽  
Yuanyang Yu ◽  
Fukun Zhao
Keyword(s):  
Small Parameter ◽  
Critical Exponent ◽  
Ground State ◽  
Local Minimum ◽  
Fractional Laplacian ◽  
Ground State Solution ◽  
Critical Nonlinearity ◽  
Poisson System ◽  
Ground State Solutions ◽  
Concentration Behavior

We are concerned with the existence and concentration behavior of ground state solutions of the fractional Schrödinger–Poisson system with critical nonlinearity [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text], [Formula: see text], [Formula: see text] denotes the fractional Laplacian of order [Formula: see text] and satisfies [Formula: see text]. The potential [Formula: see text] is continuous and positive, and has a local minimum. We obtain a positive ground state solution for [Formula: see text] small, and we show that these ground state solutions concentrate around a local minimum of [Formula: see text] as [Formula: see text].

scholarly journals Existence of positive ground state solutions of Schrödinger–Poisson system involving negative nonlocal term and critical exponent on bounded domain

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Wenxuan Zheng ◽  
Wenbin Gan ◽  
Shibo Liu
Keyword(s):  
Critical Exponent ◽  
Bounded Domain ◽  
Ground State ◽  
Mountain Pass Theorem ◽  
Nonlocal Term ◽  
Concentration Compactness ◽  
Poisson System ◽  
Ground State Solutions ◽  
Concentration Compactness Principle ◽  
Compactness Principle

AbstractIn this paper, we prove the existence of positive ground state solutions of the Schrödinger–Poisson system involving a negative nonlocal term and critical exponent on a bounded domain. The main tools are the mountain pass theorem and the concentration compactness principle.

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.

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