A Global Minimizer for Mass-Constrained Problem Revisited

We investigate the existence of solutions to the scalar field equation −Δu=g(u)−λuinRN, with mass constraint ∫RN|u|2dx=a>0,u∈H1(RN). 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.