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| In this paper, we study the following fractional Schr\"{o}dinger equation with prescribed mass\begin{equation*}\left\{\begin{aligned}&(-\Delta)^{s}u=\lambda u+a(x)|u|^{p-2}u,\quad\text{in $\mathbb{R}^{N}$},\\&\int_{\mathbb{R}^{N}}|u|^{2}dx=c^{2},\quad u\in H^{s}(\mathbb{R}^{N}),\end{aligned}\right.\end{equation*}where $0<s<1$, $N>2s$, $2+\frac{4s}{N}<p<2_{s}^{*}:=\frac{2N}{N-2s}$, $c>0$, $\lambda\in \mathbb{R}$ and $a(x)\in C^{1}(\mathbb{R}^{N},\mathbb{R}^{+})$ is a potential function. By using a minimax principle, we prove the existence of bounded state solution for the above problem under various conditions on $a(x)$. |
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| Keywords:Fractional Schr\"{o}dinger equation; Normalized solutions; Bound state; Potential |
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