*Mathematical Methods in the Applied Sciences*A mass supercritical and Sobolev critical fractional Schrödinger system

We study the following coupled fractional Schrödinger system: $$
\bcs (-\De)^s u=\la_1
u+\mu_1|u|^{p-2}u+\beta
r_1|u|^{r_1-2}u|v|^{r_2}\quad
&\hbox{in}\;\mathbb{R}^N,
\\ (-\De)^s
v=\la_2
v+\mu_2|v|^{q-2}v+\beta
r_2|u|^{r_1}|v|^{r_2-2}v\quad
&\hbox{in}\;\mathbb{R}^N,
\\
%\int_{\mathbb{R}^N}
u^2=a\quad and\quad
\int_{\mathbb{R}^N} v^2=b,
\ecs $$ with prescribed mass \[
\int_{\mathbb{R}^N}
u^2=a\quad
\hbox{and}\quad
\int_{\mathbb{R}^N} v^2=b.
\] Here, $a, b>0$ are prescribed,
$N>2s, s>\frac{1}{2}$,
$2+\frac{4s}{N}0$ sufficiently large, a mountain
pass-type normalized solution exists provided $2\leq
N\leq 4s$ and $ 2+\frac{4s}{N}

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