Normalized solutions for double critical Schrödinger–Poisson system on the first Heisenberg group

Abstract This paper investigates the existence and multiplicity of normalized solutions of the double critical Schrödinger–Poisson system on the first Heisenberg group. Together with the truncation techniques, concentration-compactness principle, and genus theory, we establish the existence and multiplicity of normalized solutions for this system. To some extent, the results presented in this paper can be regarded as a supplement and enrichment of previous studies.