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.
Cingolani, S., Secchi, S. (2015). Semiclassical analysis for pseudo-relativistic Hartree equations. JOURNAL OF DIFFERENTIAL EQUATIONS, 258(12), 4156-4179 [10.1016/j.jde.2015.01.029].
Semiclassical analysis for pseudo-relativistic Hartree equations
SECCHI, SIMONE
2015
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
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