Dengfeng Lü, Shu-Wei Dai, Multiple solutions for fractional Schrödinger-Poisson systems with Berestycki-Lions type nonlinearities

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DOI: 10.23952/jnva.10.2026.4.05

Volume 10, Issue 4, 1 August 2026, Pages 799-814

Abstract. In this paper, we study the following fractional Schrödinger-Poisson system
$(-\Delta)^{\alpha} \psi+\lambda\phi(x)\psi=g(\psi)$ in $\mathbb{R}^{3},$
$(-\Delta)^{\beta} \phi=\lambda \psi^{2}$ in $\mathbb{R}^{3},$
where $\alpha,\beta\in(0,1)$ are constants and $\lambda>0$ is a parameter. By using a truncation technique and an auxiliary functional, we prove the existence of multiple solutions for the above system when $g$ satisfies the Berestycki-Lions type conditions via combining variational methods with genus theory.

How to Cite this Article:
D. Lü, S.W. Dai, Multiple solutions for fractional Schrödinger-Poisson systems with Berestycki-Lions type nonlinearities, J. Nonlinear Var. Anal. 10 (2026), 799-814.