Positive and sign-changing ground state solutions for a fractional critical Schrödinger–Poisson system with steep potential well
Volume 134 / 2025
Annales Polonici Mathematici 134 (2025), 119-151
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.
