Ground state solutions for Schrödinger–Poisson system with critical exponential growth in R2

2021 ◽  
Vol 120 ◽  
pp. 107340
Author(s):  
Fangfang Liao ◽  
Xiaoping Wang
Keyword(s):  
Ground State ◽  
Exponential Growth ◽  
Poisson System ◽  
Ground State Solutions ◽  
Critical Exponential Growth

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 Ground state solutions for a Kirchhoff type elliptic systems involving critical exponential growth nonlinearities

2021 ◽  
Author(s):  
Shengbing Deng ◽  
Tingting Huang
Keyword(s):  
Ground State ◽  
Exponential Growth ◽  
Elliptic Systems ◽  
Ground State Solution ◽  
State Solution ◽  
Ground State Solutions ◽  
Kirchhoff Type ◽  
Critical Exponential Growth ◽  
Growth Nonlinearities

The aim of this paper is to study the ground state solution for a Kirchhoff type elliptic systems without the Ambrosetti-Rabinowitz condition.

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

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