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• W2051570690 abstract "We study the global Cauchy problem and scattering problem for the semirelativistic Hartree‐type equation in $mathbb{R}^n$, $n ge 1$, with nonlocal nonlinearity $F(u) = lambda (|x|^{-gamma} * |u|^2)u$, $0 <gamma < n$. We prove the existence and uniqueness of global solutions for $0 < gamma < frac{2n}{n+1}$, $n ge 2$ or $gamma > 2$, $n ge 3$, and the nonexistence of asymptotically‐free solutions for $0 < gamma le 1$, $nge 3$. We also specify asymptotic behavior of solutions as the mass tends to zero and infinity." @default.
• W2051570690 created "2016-06-24" @default.
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• W2051570690 date "2006-01-01" @default.
• W2051570690 modified "2023-09-25" @default.
• W2051570690 title "On the Semirelativistic Hartree‐Type Equation" @default.
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• W2051570690 doi "https://doi.org/10.1137/060653688" @default.
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