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- W4367693762 abstract "In this paper, we investigate a class of planar Schr{o}dinger-Poisson systems with critical exponential growth. We establish conditions for the local well-posedness of the Cauchy problem in the energy space, which seems innovative as it was not discussed at all in any previous results. By introducing some new ideas and relaxing some of the classical growth assumptions on the nonlinearity, we show that such system has at least two standing waves with prescribed mass, where one is a ground state standing waves with positive energy, and the other one is a high-energy standing waves with positive energy. In addition, with the help of the local well-posedness, we show that the set of ground state standing waves is orbitally stable." @default.
- W4367693762 created "2023-05-03" @default.
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- W4367693762 date "2023-04-28" @default.
- W4367693762 modified "2023-10-16" @default.
- W4367693762 title "The planar Schrodinger--Poisson system with exponential critical growth: The local well-posedness and standing waves with prescribed mass" @default.
- W4367693762 doi "https://doi.org/10.48550/arxiv.2305.00159" @default.
- W4367693762 hasPublicationYear "2023" @default.
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