Normalized solutions for a coupled fractional Schrödinger system in low dimensions

We consider the following coupled fractional Schrödinger system: { ( − Δ ) s u + λ 1 u = μ 1 | u | 2 p − 2 u + β | v | p | u | p − 2 u , ( − Δ ) s v + λ 2 v = μ 2 | v | 2 p − 2 v + β | u | p | v | p − 2 v in R N , with 0 < s < 1 , 2 s < N ≤ 4 s and 1 + 2 s N < p < N N − 2 s , under the following constraint: ∫ R N | u | 2 d x = a 1 2 and ∫ R N | v | 2 d x = a 2 2 . Assuming that the parameters μ 1 , μ 2 , a 1 , a 2 are fixed quantities, we prove the existence of normalized solution for different ranges of the coupling parameter β > 0 .