Normalized solutions to Sobolev critical Schrödinger equations with potential V(x)

In this paper, we study normalized solutions of the Schrödinger equation with Sobolev critical nonlinearity −Δu−V(x)u=λu+|u|2*−2uu∈H1(RN),λ∈R,∫RNu2=ρ2, where N ≥ 3 and 2*≔2NN−2. We prove existence of normalized solutions of the problem under different conditions on the potential V(x). Our results extend some results of Bartsch et al. [Commun. Partial Differ. Equations 46, 1729–1756 (2021)] and Molle et al. [J. Differ. Equations 333, 302–331 (2022)] to the Sobolev critical case.