Existence of normalized solutions for semilinear elliptic systems with potential.

In this paper, we consider the existence of normalized solutions to the following system: −Δu + V1(x)u + λu = μ1u3 + βv2u and −Δv + V2(x)v + λv = μ2v3 + βu2v in R 3 , under the mass constraint ∫ R 3 u 2 + v 2 = ρ 2 , where ρ is prescribed, μi, β > 0 (i = 1, 2), and λ ∈ R appears as a Lagrange multiplier. Then, by a min–max argument, we show the existence of fully nontrivial normalized solutions under various conditions on the potential V i : R 3 → R (i = 1 , 2). [ABSTRACT FROM AUTHOR]