A Global Minimizer for Mass-Constrained Problem Revisited.

We investigate the existence of solutions to the scalar field equation − Δ u = g (u) − λ u in R N , with mass constraint ∫ R N | u | 2 d x = a > 0 , u ∈ H 1 (R N). Here, N ≥ 3 ; g is a continuous function satisfying the conditions of the Berestycki–Lions type; λ is a Lagrange multiplier. Our results supplement and generalize some of the results in L. Jeanjean, S.-S. Lu, Calc. Var. Partial Differential Equations. 61 (2022), Paper No. 214, 18, and J. Hirata, K. Tanaka, Adv. Nonlinear Stud. 19 (2019), 263–290. [ABSTRACT FROM AUTHOR]