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This paper is concerned with the following Choquard equation with perturbation: - Δ u + V ( x ) u = ( 1 / | x | α ∗ | u | p ) | u | p - 2 u + g ( x ) , u ∈ H 1 ( R N ) , where N ≥ 3 , α ∈ ( 0 , N ) , and 2 - ( α / N ) < p < ( 2 N - α ) / ( N - 2 ) . This kind of equations is well known as the Choquard or nonlinear Schrödinger-Newton equation. Under some assumptions for the functions V ( x ) , we prove the existence of multiple positive solutions of the equation. Moreover, we also show that these results still hold for more generalized Choquard equation with perturbation.

Existence of Multiple Positive Solutions for Choquard Equation with Perturbation