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On the semi-relativistic Hartree type equation

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 Title: On the semi-relativistic Hartree type equation Authors: Cho, Yonggeun Browse this author Ozawa, Tohru Browse this author Keywords: semi-relativistic Hartree type equation global solution scattering non-existence of asymptotically free solution Issue Date: 2006 Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 773 Start Page: 1 End Page: 16 Abstract: We study the global Cauchy problem and scattering problem for the semi-relativistic 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 non-existence of asymptotically free solutions for $0 < \gamma \le 1, n\ge 3$. We also specify asymptotic behavior of solutions as the mass tends to zero and infinity. Type: bulletin (article) URI: http://hdl.handle.net/2115/69581 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics