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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2019-08-01
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Online Access: | https://doi.org/10.1515/anona-2020-0028 |
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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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1717769709537984512 |