arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1801.09595math.AP
收藏

几类耦合非局域分数色散偏微分方程的基态

Ground states of some coupled nonlocal fractional dispersive PDEs

Eduardo Colorado

阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

我们证明了下列耦合分数阶色散方程定态系统基态解的存在性：非线性分数阶薛定谔（NLFS）方程（对于$n=1,\, 2,\, 3$）或NLFS和分数阶Korteweg-de Vries方程（对于$n=1$），$$ \left \{ \begin{array}{ll} (-Δ)^{s} u+ λ_1 u &= u_1^{3}+βuv,\quad u\in W^{s,2}(\mathbb{R}^n), (-Δ)^{s} v + λ_2 v &= \frac 12 v^{2}+\frac 12 βu^2,\quad v\in W^{s,2}(\mathbb{R}^n), \end{array} \right. $$其中$λ_j>0$，$j=1,2$，$β\in \mathbb{R}$，$n=1,\, 2,\, 3$，和$\frac n4< s<1$ .准确地说，我们证明了任何$β>0$的正径向对称基态的存在性。

英文摘要：

We show the existence of ground state solutions to the following stationary system coming from some coupled fractional dispersive equations such as: nonlinear fractional Schrödinger (NLFS) equations (for dimension $n=1,\, 2,\, 3$) or NLFS and fractional Korteweg-de Vries equations (for $n=1$), $$ \left \{ \begin{array}{ll} (-Δ)^{s} u+ λ_1 u &= u_1^{3}+βuv,\quad u\in W^{s,2}(\mathbb{R}^n), (-Δ)^{s} v + λ_2 v &= \frac 12 v^{2}+\frac 12 βu^2,\quad v\in W^{s,2}(\mathbb{R}^n), \end{array} \right. $$ where $λ_j>0$, $j=1,2$, $β\in \mathbb{R}$, $n=1,\, 2,\, 3$, and $\frac n4< s<1$. Precisely, we prove the existence of a positive radially symmetric ground state for any $β>0$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑