On a logarithmic Hartree equation

On a logarithmic Hartree equation

We study the existence of radially symmetric solutions for a nonlinear planar Schrödinger-Poisson system in presence of a superlinear reaction term which doesn’t satisfy the Ambrosetti-Rabinowitz condition. The system is re-written as a nonlinear Hartree equation with a logarithmic convolution term,...

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Bibliographic Details
Main Authors: Bernini Federico, Mugnai Dimitri
Format: Article
Language:English
Published: De Gruyter 2019-08-01
Series:Advances in Nonlinear Analysis
Subjects:
planar schrödinger-poisson system
logarithmic hartree equation
hardy-littlewood-sobolev inequality
superlinear source
35j50
35q40
Online Access:https://doi.org/10.1515/anona-2020-0028
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spelling doaj-a627cbd8ccef4d80bb61a1ff5f38ccc12021-09-06T19:39:56ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2019-08-019185086510.1515/anona-2020-0028anona-2020-0028On a logarithmic Hartree equationBernini Federico0Mugnai Dimitri1Department of Mathematics and Applications, University of Milano - Bicocca, Via R. Cozzi 55, 20125, Milano, ItalyDepartment of Ecology and Biology (DEB), Tuscia University, Largo dell’Università, 01100, Viterbo, ItalyWe study the existence of radially symmetric solutions for a nonlinear planar Schrödinger-Poisson system in presence of a superlinear reaction term which doesn’t satisfy the Ambrosetti-Rabinowitz condition. The system is re-written as a nonlinear Hartree equation with a logarithmic convolution term, and the existence of a positive and a negative solution is established via critical point theory.https://doi.org/10.1515/anona-2020-0028planar schrödinger-poisson systemlogarithmic hartree equationhardy-littlewood-sobolev inequalitysuperlinear source35j5035q40
collection DOAJ
language English
format Article
sources DOAJ
author Bernini Federico
Mugnai Dimitri
spellingShingle Bernini Federico
Mugnai Dimitri
On a logarithmic Hartree equation
Advances in Nonlinear Analysis
planar schrödinger-poisson system
logarithmic hartree equation
hardy-littlewood-sobolev inequality
superlinear source
35j50
35q40
author_facet Bernini Federico
Mugnai Dimitri
author_sort Bernini Federico
title On a logarithmic Hartree equation
title_short On a logarithmic Hartree equation
title_full On a logarithmic Hartree equation
title_fullStr On a logarithmic Hartree equation
title_full_unstemmed On a logarithmic Hartree equation
title_sort on a logarithmic hartree equation
publisher De Gruyter
series Advances in Nonlinear Analysis
issn 2191-950X
publishDate 2019-08-01
description We study the existence of radially symmetric solutions for a nonlinear planar Schrödinger-Poisson system in presence of a superlinear reaction term which doesn’t satisfy the Ambrosetti-Rabinowitz condition. The system is re-written as a nonlinear Hartree equation with a logarithmic convolution term, and the existence of a positive and a negative solution is established via critical point theory.
topic planar schrödinger-poisson system
logarithmic hartree equation
hardy-littlewood-sobolev inequality
superlinear source
35j50
35q40
url https://doi.org/10.1515/anona-2020-0028
work_keys_str_mv AT berninifederico onalogarithmichartreeequation
AT mugnaidimitri onalogarithmichartreeequation
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