Funkcialaj Ekvacioj
Print ISSN : 0532-8721
On the Cauchy Problem of Fractional Schrödinger Equation with Hartree Type Nonlinearity
Yonggeun ChoHichem HajaiejGyeongha HwangTohru Ozawa
Author information
JOURNALS FREE ACCESS

2013 Volume 56 Issue 2 Pages 193-224

Details
Abstract

We study the Cauchy problem for the fractional Schrödinger equation itu = (m2−Δ)α/2u + F(u) in R1+n, where n ≥ 1, m ≥ 0, 1 < α < 2, and F stands for the nonlinearity of Hartree type F(u) = λ (ψ (·) |·|−γ ∗ |u|2)u with λ = ±1, 0 < γ < n, and 0 ≤ ψ ∈ L (Rn). We prove the existence and uniqueness of local and global solutions for certain α, γ, λ, ψ. We also remark on finite time blowup of solutions when λ = −1.

Information related to the author
© 2013 by the Division of Functional Equations, The Mathematical Society of Japan
Previous article Next article
feedback
Top