scholarly journals Infinitely many positive solutions for a Schrödinger–Poisson system

2011 ◽  
Vol 74 (16) ◽  
pp. 5705-5721 ◽  
Author(s):  
Pietro d’Avenia ◽  
Alessio Pomponio ◽  
Giusi Vaira
Keyword(s):  
Positive Solutions ◽  
Poisson System

INFINITELY MANY POSITIVE SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER–POISSON SYSTEM

2010 ◽  
Vol 12 (06) ◽  
pp. 1069-1092 ◽  
Author(s):  
GONGBAO LI ◽  
SHUANGJIE PENG ◽  
SHUSEN YAN
Keyword(s):  
Positive Solutions ◽  
Poisson System ◽  
Nonlinear Schrödinger ◽  
Positive Functions

We consider the following nonlinear Schrödinger–Poisson system in ℝ3[Formula: see text] where K(r) and Q(r) are bounded and positive functions, 1 < p < 5. Assume that K(r) and Q(r) have the following expansions (as r → +∞): [Formula: see text] where a > 0, b ∈ ℝ, m > 1/2, n > 1, θ > 0, κ > 0, and Q0 > 0 are some constants. We prove that (0.1) has infinitely many non-radial positive solutions if b < 0, or if b ≥ 0 and 2m < n.

scholarly journals Existence and Multiplicity of Positive Solutions for Schrödinger-Kirchhoff-Poisson System with Singularity

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mengjun Mu ◽  
Huiqin Lu
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Nehari Manifold ◽  
Poisson System ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions ◽  
The Nehari Manifold

We study a singular Schrödinger-Kirchhoff-Poisson system by the variational methods and the Nehari manifold and we prove the existence, uniqueness, and multiplicity of positive solutions of the problem under different conditions.

scholarly journals Positive solutions for a nonlinear Schrödinger-Poisson system

2018 ◽  
Vol 38 (11) ◽  
pp. 5461-5504 ◽  
Author(s):  
Chunhua Wang ◽  
◽  
Jing Yang ◽  
Keyword(s):  
Positive Solutions ◽  
Poisson System ◽  
Nonlinear Schrödinger
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