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- Title
Existence of normalized solutions for Schrödinger systems with linear and nonlinear couplings.
- Authors
Yun, Zhaoyang; Zhang, Zhitao
- Abstract
In this paper we study the nonlinear Bose–Einstein condensates Schrödinger system { − Δ u 1 − λ 1 u 1 = μ 1 u 1 3 + β u 1 u 2 2 + κ (x) u 2 in R 3 , − Δ u 2 − λ 2 u 2 = μ 2 u 2 3 + β u 1 2 u 2 + κ (x) u 1 in R 3 , ∫ R 3 u 1 2 = a 1 2 , ∫ R 3 u 2 2 = a 2 2 , where a 1 , a 2 , μ 1 , μ 2 , κ = κ (x) > 0 , β < 0 , and λ 1 , λ 2 are Lagrangian multipliers. We use the Ekeland variational principle and the minimax method on manifold to prove that this system has a solution that is radially symmetric and positive.
- Subjects
BOSE Corp.; BOSE-Einstein condensation; NONLINEAR systems; VARIATIONAL principles; EINSTEIN manifolds; LINEAR systems
- Publication
Boundary Value Problems, 2024, Vol 2024, Issue 1, p1
- ISSN
1687-2762
- Publication type
Article
- DOI
10.1186/s13661-024-01830-w