On the semirelativistic Hartree type equation
Preprint Series # 773 Cho, Yonggeun and Ozawa, Tohru On the semirelativistic Hartree type equation. (2006); AbstractWe study the global Cauchy problem and scattering problem for the semirelativistic 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 nonexistence 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.
Item Type:  Preprint 

Additional Information:  10 

Uncontrolled Keywords:  semirelativistic Hartree type equation, global solution,
scattering, nonexistence of asymptotically free solution 

Subjects:  35xx PARTIAL DIFFERENTIAL EQUATIONS 

ID Code:  1511 

