Semiclassical analysis for pseudo-relativistic Hartree equations
نویسندگان
چکیده
In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation √ −ε2∆ +m2u+ V u = (Iα ∗ |u|) |u|p−2u, in R , where m > 0, 2 ≤ p < 2N N−1 , V : R N → 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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