论文标题
分数对数schrödinger方程的半经典状态
Semiclassical states for fractional logarithmic Schrödinger equations
论文作者
论文摘要
在本文中，我们考虑以下分数对数schrödinger方程\ begin {equination*} \ varepsilon^{2S}（ - δ）^s u + v（x） $ n \ ge 1 $，$ v（x）\ in C（\ r^n，[ - 1，+\ infty））$。通过引入一个有趣的惩罚功能，我们表明该问题具有阳性解决方案$ u _ {\ varepsilon} $，以$ \ varepsilon \ to $ \ varepsilon \ to 0 $，以$ v $的本地最低为$ v $。 $ V $的衰减率没有限制，尤其是可以紧凑的支持。
In this paper, we consider the following fractional logarithmic Schrödinger equation \begin{equation*} \varepsilon^{2s}(-Δ)^s u + V(x)u=u\log |u|^2\ \ \text{in}\ \R^N, \end{equation*} where $\varepsilon>0$, $N\ge 1$, $V(x)\in C(\R^N,[-1,+\infty))$. By introducing an interesting penalized function, we show that the problem has a positive solution $u_{\varepsilon}$ concentrating at a local minimum of $V$ as $\varepsilon\to 0$. There is no restriction on decay rates of $V$, especially it can be compactly supported.
