LAUSR

Abstract In this paper, we study the existence of nodal solutions for the following fractional Choquard equation ( − △ ) α u + u = ∫ R N | u ( z ) | p | x − z | μ d z | u ( x ) | p − 2 u ( x ) , x ∈ R N , where 0 μ 2 α N and 2 N − μ N − 1 p 2 N − μ N − 2 α with α ∈ ( 1 2 , 1 ) . In view of the nonlocality of the fractional Laplacian operator and the so-called Hartree term ∫ R N | u ( z ) | p | x − z | μ d z | u ( x ) | p − 2 u ( x ) , the corresponding variational functional has entirely different properties with respect to the Laplacian case. For any k ∈ N , we prove that the problem possesses at least a radially symmetrical solution which changes sign k times.