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A mass supercritical and Sobolev critical fractional Schrödinger system
  • Meiqi Liu,
  • Quanqing Li
Meiqi Liu
Tsinghua University Department of Mathematical Sciences

Corresponding Author:[email protected]

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Quanqing Li
Honghe University
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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}
28 Oct 2021Submitted to Mathematical Methods in the Applied Sciences
29 Oct 2021Submission Checks Completed
29 Oct 2021Assigned to Editor
13 Nov 2021Reviewer(s) Assigned
13 Dec 2021Review(s) Completed, Editorial Evaluation Pending
17 Dec 2021Editorial Decision: Revise Major
13 Mar 20221st Revision Received
14 Mar 2022Assigned to Editor
14 Mar 2022Submission Checks Completed
14 Mar 2022Reviewer(s) Assigned
06 May 2022Review(s) Completed, Editorial Evaluation Pending
11 May 2022Editorial Decision: Revise Major
02 Aug 20222nd Revision Received
03 Aug 2022Submission Checks Completed
03 Aug 2022Assigned to Editor
09 Aug 2022Reviewer(s) Assigned
18 Aug 2022Review(s) Completed, Editorial Evaluation Pending
19 Aug 2022Editorial Decision: Accept
16 Sep 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8696