Infinitely many nonradial positive solutions for multi-species nonlinear Schrödinger systems in [formula omitted].

In this paper, we consider the multi-species nonlinear Schrödinger systems in R N : { − Δ u j + V j (x) u j = μ j u j 3 + ∑ i = 1 ; i ≠ j d β i , j u i 2 u j in R N , u j (x) > 0 in R N , u j (x) → 0 as | x | → + ∞ , j = 1 , 2 , ⋯ , d , where N = 2 , 3 , μ j > 0 are constants, β i , j = β j , i ≠ 0 are coupling parameters, d ≥ 2 and V j (x) are potentials. By Ljapunov-Schmidt reduction arguments, we construct infinitely many nonradial positive solutions of the above system under some mild assumptions on potentials V j (x) and coupling parameters { β i , j } , without any symmetric assumptions on the limit case of the above system. Our result, giving a positive answer to the conjecture in Pistoia and Viara [50] and extending the results in [50,52] , reveals new phenomenon in the case of N = 2 and d = 2 and is almost optimal for the coupling parameters { β i , j }. [ABSTRACT FROM AUTHOR]