Multiple positive bound state solutions for a critical Choquard equation

In this paper we consider the problem {document}$ (Pλ)\ \ \ \ \ \ \{ {array}{rcl} -Δ u+Vλ(x)u = (Iμ*|u|^{2*μ})|u|^{2*μ-2}u \ \ in \ \ RN, \\ u>0 \ \ in \ \ RN, {array} . document where document Vλ = λ+V₀ document with document λ ≥ 0 document , document V_0∈ LN/2({R}^N) document , document Iμ = 1/|x|^μ document is the Riesz potential with document 0<μ<min\{N, 4\} document and document 2*μ = 2N-μ/N-2 document with document N≥ 3 document . Under some smallness assumption on document V_0 document and document λ document we prove the existence of two positive solutions of document (P_λ) ${document} . In order to prove the main results, we used variational methods combined with degree theory.