Positive least energy solutions and phase separation for coupled Schrödinger equations with critical exponent: higher dimensional case

• Published in: Calculus of variations and partial differential equations Vol. 52; no. 1-2; pp. 423 - 467
• Main Authors: Chen, Zhijie, Zou, Wenming
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2015; Springer Nature B.V
• Subjects: Analysis; Applied mathematics; Bose-Einstein condensates; Calculus of variations; Calculus of Variations and Optimal Control; Optimization; Classification; Control; Dirichlet problem; Eigenvalues; Exponents; Mathematical analysis; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Partial differential equations; Phase separation; Schrodinger equation; Schroedinger equation; Systems Theory; Texts; Theoretical; 35J50; 35B40

We study the following nonlinear Schrödinger system which is related to Bose–Einstein condensate: - Δ u + λ 1 u = μ 1 u 2 ∗ - 1 + β u 2 ∗ 2 - 1 v 2 ∗ 2 , x ∈ Ω , - Δ v + λ 2 v = μ 2 v 2 ∗ - 1 + β v 2 ∗ 2 - 1 u 2 ∗ 2 , x ∈ Ω , u ≥ 0 , v ≥ 0 in Ω , u = v = 0 on ∂ Ω . Here Ω ⊂ R N is a smooth bounded d...