Semiclassical analysis for pseudo-relativistic Hartree equations
Semiclassical analysis for pseudo-relativistic Hartree equations
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DOI：
10.1016/j.jde.2015.01.029
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发表时间：
2015-01
影响因子：
2.4
通讯作者：
S. Cingolani;S. Secchi
中科院分区：
文献类型：
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作者：
S. Cingolani;S. Secchi
本文研究了伪相对论性Hartree方程−ε2Δ+m 2 u+Vu=(iα⁎|u|p)|u|p−2 u，在RN中的半经典极限，其中m>；0，2≤p<；2 N N−1，V：R N→R是外标量势，iα(X)=c N，α|x|N−α是卷积核，c N，α是正常数，(N−1)p−N<；α<；当N=3，α=p=2时，我们的方程变成了具有库仑核的伪相对论Hartree方程。
In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation− ε 2 Δ+ m 2 u+ V u=(I α⁎| u| p)| u| p− 2 u, in R N, where m> 0, 2≤ p< 2 N N− 1, V: R N→ R is an external scalar potential, I α (x)= c N, α| x| N− α is a convolution kernel, c N, 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.