id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-532	Deng, Jin; Xia,  Aliang; Yang, Jianfu	Positive vortex solutions and phase separation for coupled Schrodinger system with singular potential	2020	20	.pdf	application/pdf	7953	454	87	= Eβn(un, vn) ≤ I∞ for all n ∈ N. So, after passing to a subsequence, there exist u∞, v∞ ∈ H such that (un, vn) ⇀ (u∞, v∞) weakly in H, (un, vn)→ (u∞, v∞) strongly in L4(R2)× L4(R2), (un, vn)→ (u∞, v∞) a.e. in R2 × R2. ∇v − v∆θ = 0, x ∈ RN , u, v ≥ 0, x ∈ RN . (1.4) If we assume u(x) = u(|x|) and choose the angular coordinate in R2 as phase function, see [3, 4], that is, θ(x) :=  arctan x2 x1 , if x1 > 0, π + arctan x2 x1 , if x1 < 0, π/2, if x1 = 0 and x2 > 0, −π/2, if x1 = 0 and x2 < 0, (1.5) we obtain ∆θ = 0, ∇θ · ∇u = 0, |∇θ|2 = 1 |x|2 , EJDE-2020/108 SCHRÖDINGER SYSTEM WITH SINGULAR POTENTIAL 3 and the system reduces to −∆u+ λ1u+ k2 0 u |x|2 = µ1u 3 + βuv2, x ∈ R2, −∆v + λ2v + k2 0 v |x|2 = µ2v 3 + βu2v, x ∈ R2, u, v ≥ 0, x ∈ R2.	cache/ejde-532.pdf	txt/ejde-532.txt