论文标题
schrödinger系统的归一化解决方案二维的解决方案
Normalized solutions for Schrödinger systems in dimension two
论文作者
论文摘要
在本文中，我们研究了具有指数增长的以下非线性schrödinger系统的归一化解决方案\ begin {align*} \ left \ {\ strag {Aligned}＆-ΔU+λ_{1} u = h_ {u}（u，v），\ quad \ quad \ quad \ quad \ hbox {in} \ hbox {in} \ Mathbb {r}^{2}，\\＆\ int _ {\ MathBb {r}^{2}}}} | u |^{2} dx = a^a^{2}，\ quad，\ quad \ int _ {\ mathbb {r}^{2}} | v |^{2} dx = b^{2}，\ end {aligned} \ right。 \ end {align*}其中规定了$ a，b> 0 $，$λ_{1}，λ_{2} \ in \ mathbb {r} $和函数$ h_ {u}，h_ {u {v} $是carathéodory函数$ h $ h_ $ h______________ $ \ mathbb {r}^{2} $。对于$ \ mathbb {r}^{2} $，我们的主要结果对于SchrödingerSystems来说是全新的。使用Pohozaev歧管和变异方法，我们确定了上述问题的归一化解决方案。
In this paper, we study the existence of normalized solutions to the following nonlinear Schrödinger systems with exponential growth \begin{align*} \left\{ \begin{aligned} &-Δu+λ_{1}u=H_{u}(u,v), \quad \quad \hbox{in }\mathbb{R}^{2},\\ &-Δv+λ_{2} v=H_{v}(u,v), \quad \quad \hbox{in }\mathbb{R}^{2},\\ &\int_{\mathbb{R}^{2}}|u|^{2}dx=a^{2},\quad \int_{\mathbb{R}^{2}}|v|^{2}dx=b^{2}, \end{aligned} \right. \end{align*} where $a,b>0$ are prescribed, $λ_{1},λ_{2}\in \mathbb{R}$ and the functions $H_{u},H_{v}$ are partial derivatives of a Carathéodory function $H$ with $H_{u},H_{v}$ have exponential growth in $\mathbb{R}^{2}$. Our main results are totally new for Schrödinger systems in $\mathbb{R}^{2}$. Using the Pohozaev manifold and variational methods, we establish the existence of normalized solutions to the above problem.
