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On radial solutions of semi-relativistic Hartree equations
Title: | On radial solutions of semi-relativistic Hartree equations |
Authors: | Cho, Yonggeun Browse this author | Ozawa, Tohru Browse this author |
Keywords: | semi-relativistic Hartree type equation | global well-posedness | radially symmetric solution |
Issue Date: | 2006 |
Publisher: | Department of Mathematics, Hokkaido University |
Journal Title: | Hokkaido University Preprint Series in Mathematics |
Volume: | 792 |
Start Page: | 1 |
End Page: | 10 |
Abstract: | We consider the semi-relativistic Hartree type equation with nonlocal nonlinearity $F(u) = \lambda (|x|^{-\gamma} * |u|^2)u, 0 < \gamma < n, n \ge 1$. In \cite{chooz2}, the global well-posedness (GWP) was shown for the value of $\gamma \in (0, \frac{2n}{n+1}), n \ge 2$ with large data and $\gamma \in (2, n), n \ge 3$ with small data. In this paper, we extend the previous GWP result to the case for $\gamma \in (1, \frac{2n-1}n), n \ge 2$ with radially symmetric large data. Solutions in a weighted Sobolev space are also studied. |
Type: | bulletin (article) |
URI: | http://hdl.handle.net/2115/69600 |
Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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