Multiplicity and concentration properties for (p,q)-Kirchhoff non-autonomous problems with Choquard nonlinearity

n this paper, we study the following (p,q)-Kirchhoff problem with Choquard nonlinearity: −(1+a∫RN|∇u|pdx)Δpu−(1+b∫RN|∇u|qdx)Δqu+Vε(x)(|u|p−2u+|u|q−2u)=(|x|−μ⁎F(u))f(u)inRN, where ε is a small positive parameter, a,b are positive constants, 1