On the semirelativistic Hartree-type equation

Yonggeun Cho*, Tohru Ozawa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

66 Citations (Scopus)


We study the global Cauchy problem and scattering problem for the semirelativistic Hartree-type equation in ℝn, n ≥ 1, with nonlocal nonlinearity F(u) = λ(|x| * |u| 2)u, 0 < γ < n. We prove the existence and uniqueness of global solutions for 0 < γ < 2n/n+1, n ≥ 2 or γ > 2, n ≥ 3, and the nonexistence of asymptotically-free solutions for 0 < γ ≤ 1, n ≥ 3. We also specify asymptotic behavior of solutions as the mass tends to zero and infinity.

Original languageEnglish
Pages (from-to)1060-1074
Number of pages15
JournalSIAM Journal on Mathematical Analysis
Issue number4
Publication statusPublished - 2006
Externally publishedYes


  • Global solution
  • Nonexistence of asymptotically free solutions
  • Scattering
  • Semirelativistic Hartree-type equation

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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