Abstract
In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation−ε2Δ+m2u+Vu=(Iα⁎|u|p)|u|p−2u,in RN, where m>0, 2≤p<2NN−1, V:RN→R is an external scalar potential, Iα(x)=cN,α|x|N−α is a convolution kernel, cN,α is a positive constant and (N−1)p−N<α<N. For N=3, α=p=2, our equation becomes the pseudo-relativistic Hartree equation with Coulomb kernel.
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