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.

Related Organizations

Guizhou University
China (People's Republic of)

Keywords

global minimizers, Berestycki–Lions conditions, variational methods, QA1-939, Schrödinger equations, normalized solution, Mathematics

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