Groundstates of the planar Schrodinger-Poisson system with potential well and lack of symmetry
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Date
2023-06-06
ORCID
0000-0003-4615-5537Advisor
Referee
Mark
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Cambridge University Press
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Abstract
The Schrodinger-Poisson system describes standing waves for the nonlinear Schrodinger equation interacting with the electrostatic field. In this paper, we are concerned with the existence of positive ground states to the planar Schrodinger-Poisson system with a nonlinearity having either a subcritical or a critical exponential growth in the sense of Trudinger-Moser. A feature of this paper is that neither the finite steep potential nor the reaction satisfies any symmetry or periodicity hypotheses. The analysis developed in this paper seems to be the first attempt in the study of planar Schrodinger-Poisson systems with lack of symmetry.
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PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS. 2023, vol. 117, issue 128, p. 1-31.
https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/groundstates-of-the-planar-schrodingerpoisson-system-with-potential-well-and-lack-of-symmetry/223939198AEDB4F9B7DCB633917950DD
https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/groundstates-of-the-planar-schrodingerpoisson-system-with-potential-well-and-lack-of-symmetry/223939198AEDB4F9B7DCB633917950DD
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Peer-reviewed
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en