Existence of a Positive Solution for a Class of Choquard Equation with Upper Critical Exponent

In this paper, we investigate the existence of nontrivial solution for the following class of Choquard equation where N ∈ N , N ≥ 3 , α ∈ ( 0 , N ) , I α is a Riesz potential, λ > 0 is a parameter, p = N + α N - 2 is the upper Hardy–Littlewood–Sobolev critical exponent and q ∈ ( 2 , 2 N N - 2 ) . We prove that there exists λ 0 > 0 such that for λ ≥ λ 0 , problem (1) possesses one positive radial solution.