Abstract
This paper is concerned with the following Choquard equation with perturbation:-Δu+V(x)u=(1/|x|α∗|u|p)|u|p-2u+g(x),u∈H1(RN), whereN≥3,α∈(0,N), and2-(α/N)<p<(2N-α)/(N-2). This kind of equations is well known as the Choquard or nonlinear Schrödinger-Newton equation. Under some assumptions for the functionsV(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.
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