In this paper, we consider the following nonlinear Choquard equation -ε2Δw V(x)w=ε-θ(Y1(w) Y2(w)), where ε>0, N>2, Y1(w):=W1(x)[Iθ*(W1|w|p)]|w|p-2w, Y2(w):=W2(x)[Iθ*(W2|w|q)]|w|q-2w, Iθ is the Riesz potential with order Θ∈(0,N), and infRNWi>0, i=1,2. By imposing suitable assumptions to V(x),
Wi(x), i=1,2, we establish the multiplicity of semiclassical solutions by using pseudo-index theory and the existence of groundstate solutions by Nehari method. Moreover, the convergence and concentration of the positive groundstate solution are discussed.
Cite this paper
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