Normalized Solutions for a Sobolev Critical Fractional Schrodinger-Poisson System

In this paper, we study the existence of normalized solutions for the fractional critical Schrodinger-Poisson system {(-Delta)(s)u+gamma phi u=lambda u+mu|u|(q-2)u+|u|(2s & lowast;-2)u, in R-3, (-Delta)(t)phi=u(2), in R-3, with the prescribed L-2 norm integral(R3)|u|(2)dx=a(2), where s,t is an element of(0,1) satisfies 2s+2t>3,q is an element of(2,2s & lowast;),a>0 and gamma,mu>0 are parameters. We establish several existence results for the L-2-subcritical regime, i.e., q is an element of(2,2+2(3-2t)/ 3); the L-2-critical regime, i.e., q=2+4s/3, and the L-2-supercritical regime, i.e., q is an element of(2+4s/3,2s & lowast;). These cases are studied under different assumptions imposed on the parameters gamma,mu and the mass a, respectively. To prove the above conclusions, we comprehensively apply the Jeanjean's theory, Pohozaev manifold method and Brezis-Nirenberg's technique skill to overcome the lack of compactness. This paper complements the paper by He, Meng and Squassina (Calc Var PDE, 63(6): 142, 2024); and the paper by Li and Teng (Mediterr J Math, 20(2):92, 2023), since we consider the normalized solutions of the fractional Schrodinger-Poisson problems with the Sobolev critical term, and the perturbation mu|u|(q-2)u is allowed to have L-2-critical growth, i.e., q=2+4s/3.