Localized nodal solutions for system of critical Choquard equations

In this paper, we study the system of critical Choquard equations iota epsilon 2 increment vj - a(x)vj + n-ary sumation k i=1 beta ij epsilon-alpha(f ) RN |vi(y)|2*alpha dy |vj|2*alpha-2vj + lambda j|vj|q-2vj = 0, x is an element of RN, |x-y|N-alpha vj(x) -> 0 as |x| -> infinity, j= 1, . . . , k, where N >= 3, lambda j > 0, j = 1, ... , k, (N - 4)+ < alpha < N, 2*alpha = N+alpha N-2 , max{2, 2* - 1} < q < 2* = 2N N-2, epsilon > 0 is a small parameter and the potential function a is bounded and positive. By the truncation method and the method of invariant sets of descending flow, we establish for small epsilon the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function a.(c) 2023 Elsevier B.V. All rights reserved.