On radial solutions of semirelativistic Hartree equations
Preprint Series # 792 Cho, Yonggeun and Ozawa, Tohru On radial solutions of semirelativistic Hartree equations. (2006); AbstractWe consider the semirelativistic 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 wellposedness
(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 $\gamma \in (1, \frac{2n1}n), n \ge 2$ with radially symmetric
large data. Solutions in a weighted Sobolev space are also studied. Item Type:  Preprint 

Additional Information:  20 

Uncontrolled Keywords:  semirelativistic Hartree type equation, global
wellposedness, radially symmetric solution 

Subjects:  35xx PARTIAL DIFFERENTIAL EQUATIONS 

ID Code:  1553 

