Normalized ground state for the Sobolev critical Schrödinger equation involving Hardy term with combined nonlinearities

Abstract In this paper, we study the existence and properties of normalized solutions for the following Sobolev critical Schrödinger equation involving Hardy term: with prescribed mass where 2* is the Sobolev critical exponent. For a L 2 ‐subcritical, L 2 ‐critical, or L 2 ‐supercritical perturbation , we prove several existence results of normalized ground state when and non‐existence results when . Furthermore, we also consider the asymptotic behavior of the normalized solutions u as or .