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Positive and sign-changing ground state solutions for a fractional critical Schrödinger–Poisson system with steep potential well

Jiao Fu, Jia-Feng Liao Annales Polonici Mathematici MSC: Primary 35J20; Secondary 35B33, 35J60 DOI: 10.4064/ap240802-2-6 Published online: 28 July 2025

Abstract

We investigate a class of fractional Schrödinger–Poisson systems with critical exponents and steep potential well. By using the constraint variational method and a quantitative deformation lemma, the existence of positive ground state solutions and sign-changing ground state solutions is obtained. It is shown that the energy of the sign-changing ground state solution is strictly larger than twice the energy of the positive ground state solution. Moreover, we also study the asymptotic behavior of the sign-changing ground state solution.

Authors

  • Jiao FuSchool of Mathematics and Information
    China West Normal University
    637009 Nanchong, China
    e-mail
  • Jia-Feng LiaoSchool of Mathematics and Information
    China West Normal University
    637009 Nanchong, China
    and
    College of Mathematics Education
    China West Normal University
    637009 Nanchong, China
    e-mail

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