Normalized solutions for Schrödinger equations with potentials and general nonlinearities.

In this paper, we are concerned with the nonlinear Schrödinger equation - Δ u + V (x) u + λ u = g (u) in R N , λ ∈ R , with prescribed L 2 -norm ∫ R N u 2 d x = ρ 2 and lim | x | → + ∞ V (x) = : V ∞ ≤ + ∞ under general assumptions on g which allows at least mass critical growth. For the case of V ∞ < ∞ , including singular potential, the sufficient conditions are given for the existence of a ground state solution by developing the minimization methods with constraints proposed in Bieganowski and Mederski (J Funct Anal 280(11):108989, 2021) and a delicate analysis of estimates on the least energy comparing with the limiting functional. While for the trapping case V ∞ = ∞ , the existence of a ground state solution as well as a second solution of mountain pass type is established. [ABSTRACT FROM AUTHOR]