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1 results

  • Groundstates of the planar Schrödinger–Poisson system with potential well and lack of symmetry

  • Part of
  • Zhisu Liu, Vicenţiu D. Rădulescu, Jianjun Zhang
  • Journal:
    Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 154 / Issue 4 / August 2024
    Published online by Cambridge University Press:
    22 May 2023, pp. 993-1023
    Print publication:
    August 2024
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  • The Schrödinger–Poisson system describes standing waves for the nonlinear Schrödinger equation interacting with the electrostatic field. In this paper, we are concerned with the existence of positive ground states to the planar Schrödinger–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 Schrödinger–Poisson systems with lack of symmetry.