scholarly journals Schrödinger–Poisson systems with a general critical nonlinearity

2016 ◽  
Vol 19 (04) ◽  
pp. 1650028 ◽  
Author(s):  
Jianjun Zhang ◽  
João Marcos do Ó ◽  
Marco Squassina
Keyword(s):  
Positive Solutions ◽  
Critical Growth ◽  
Critical Nonlinearity ◽  
Poisson System ◽  
Asymptotics Of Solutions ◽  
Existence Of Positive Solutions ◽  
General Nonlinearity

We consider a Schrödinger–Poisson system involving a general nonlinearity at critical growth and we prove the existence of positive solutions. The Ambrosetti–Rabinowitz condition is not required. We also study the asymptotics of solutions with respect to a parameter.

scholarly journals Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity

2016 ◽  
Vol 16 (1) ◽  
pp. 15-30 ◽  
Author(s):  
Jianjun Zhang ◽  
João Marcos do Ó ◽  
Marco Squassina
Keyword(s):  
Positive Solutions ◽  
Critical Case ◽  
Perturbation Approach ◽  
Critical Nonlinearity ◽  
Poisson System ◽  
Asymptotics Of Solutions ◽  
Existence Of Positive Solutions ◽  
General Nonlinearity

AbstractWe consider a fractional Schrödinger–Poisson system with a general nonlinearity in the subcritical and critical case. The Ambrosetti–Rabinowitz condition is not required. By using a perturbation approach, we prove the existence of positive solutions. Moreover, we study the asymptotics of solutions for a vanishing parameter.

scholarly journals Positive solutions of critical quasilinear elliptic problems in general domains

1998 ◽  
Vol 3 (1-2) ◽  
pp. 65-84 ◽  
Author(s):  
Filippo Gazzola
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Unbounded Domains ◽  
Critical Growth ◽  
Quasilinear Elliptic Equations ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

We consider a certain class of quasilinear elliptic equations with a term in the critical growth range. We prove the existence of positive solutions in bounded and unbounded domains. The proofs involve several generalizations of standard variational arguments.

scholarly journals Positive Solutions for Schrödinger-Poisson Systems with Sign-Changing Potential and Critical Growth

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Pengfei He ◽  
Hongmin Suo
Keyword(s):  
Variational Method ◽  
Positive Solutions ◽  
Critical Growth ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Multiplicity Of Positive Solutions

In this paper, we study the existence of positive solutions for Schrödinger-Poisson systems with sign-changing potential and critical growth. By using the analytic techniques and variational method, the existence and multiplicity of positive solutions are obtained.

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