Uniqueness of positive solutions to some Schrödinger systems. (June 2020) - Zhou, Luyan; Wang, Zhi-Qiang
Abstract: This paper is devoted to the study of the uniqueness of positive solutions of the following coupled Schrödinger equations: − Δ u + λ u = μ 1 u 3 + β v 2 u − γ v in Ω, − Δ v + λ v = μ 2 v 3 + β u 2 v − γ u in Ω, u > 0, v > 0 in Ω, u = v = 0 on ∂ Ω ( or u, v ∈ H 1 ( R N ) as Ω = R N ), where N ≤ 3, Ω ⊂ R N is a smooth domain, λ, μ 1, μ 2 are positive constants, β and γ are nonlinear and linear coupling constants respectively. We prove some new results on the uniqueness of positive solutions in several cases, improving and strengthening earlier works in the literature.