论文标题
存在Neumann条件的分数Schrödinger方程的非负溶液
Existence of nonnegative solutions for fractional Schrödinger equations with Neumann condition
论文作者
论文摘要
在本文中，我们研究了分数laplacian的诺伊曼问题，即\ begin {equination} \ left \ {\ oken {array} {rcll} {rcll} \ varepsilon^{2S} {2S} {2S}（ - δ） \ Mathcal {n} _ {s} u＆=＆0，\，\，\，\ text {in} \，\，\，\ Mathbb {r}^{n} \ backslashω\ end oden {array {array} \ right。 \ end {equation}其中$ω\ subset \ mathbb {r}^{n} $是一个平稳的界面域，$ n> 2s $，$ s \ in（0,1）$，$ \ varepsilon> 0 $ as a paramcal and $ \ nonlo deip in nontrodia ROS-OTON和VALDINOCI。我们建立了非负，非恒定的小能源解决方案$ u _ {\ varepsilon} $，我们使用Moser-nash迭代过程表明$ _ {\ varepsilon} \ in L^{\ infty}（ω）$。
In this paper we study a Neumann problem for the fractional Laplacian, namely \begin{equation}\left\{ \begin{array}{rcll} \varepsilon^{2s}(- Δ)^{s}u + u &=& f(u) \ \ &\mbox{in} \ \ Ω\\ \mathcal{N}_{s}u &=& 0 , \,\, &\text{in} \,\, \mathbb{R}^{N}\backslash Ω\end{array}\right. \end{equation} where $Ω\subset \mathbb{R}^{N}$ is a smooth bounded domain, $N>2s$, $s \in (0,1)$, $\varepsilon > 0$ is a parameter and $\mathcal{N}_{s}$ is the nonlocal normal derivative introduced by Dipierro, Ros-Oton, and Valdinoci. We establish the existence of a nonnegative, non-constant small energy solution $u_{\varepsilon}$, and we use the Moser-Nash iteration procedure to show that $u_{\varepsilon} \in L^{\infty}(Ω)$.
