scholarly journals Ground State Sign-Changing Solution for Schrödinger-Poisson System with Critical Growth

2021 ◽  
Vol 20 (2) ◽  
Author(s):  
Ziheng Zhang ◽  
Ying Wang ◽  
Rong Yuan
Keyword(s):  
Ground State ◽  
Critical Growth ◽  
Poisson System

scholarly journals Multiple positive bound states for critical Schrödinger-Poisson systems

2019 ◽  
Vol 25 ◽  
pp. 73 ◽  
Author(s):  
Giovanna Cerami ◽  
Riccardo Molle
Keyword(s):  
Variational Methods ◽  
Ground State ◽  
Bound States ◽  
Nonlinear Term ◽  
Critical Growth ◽  
Poisson System ◽  
Lack Of Compactness ◽  
Ground State Solutions ◽  
Existence And Multiplicity

Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schrödinger-Poisson system: [see formula in PDF] We remark that (SP) exhibits a “double” lack of compactness because of the unboundedness of ℝ3 and the critical growth of the nonlinear term and that in our assumptions ground state solutions of (SP) do not exist.

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