Existence of multi-bubbling solutions for a critical Hartree type equation : local Pohožaev identities methods

This paper deals with the following equation (Formula presented.) where N≥5, 5-6N-2<α≤4, 2α∗=2N-αN-2 is the so-called upper critical exponent in the Hardy-Littlewood-Sobolev inequality and K(|x′|,x′′), where (x′,x′′)∈R2×RN-2, is bounded and nonnegative. Under proper assumptions on the potential function K, we obtain the existence of infinitely many solutions for the nonlocal critical equation by using a finite dimensional reduction argument and local Pohožaev identities. It is a remarkable fact that the order of the Riesz potential influences the existence/non-existence of solutions.