On the semi-relativistic Hartree type equation

DOI IR (HANDLE) Open Access

Description

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.

Journal

Keywords

Details 詳細情報について

  • CRID
    1390853649725496448
  • NII Article ID
    120006459478
  • DOI
    10.14943/83923
  • HANDLE
    2115/69581
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • JaLC
    • IRDB
    • CiNii Articles
  • Abstract License Flag
    Allowed

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