论文标题
非线性Schrödinger方程的归一化基态解决方案涉及指数临界增长
Normalized ground state solutions of nonlinear Schrödinger equations involving exponential critical growth
论文作者
论文摘要
我们关注以下非线性schrödinger方程 开始{eqnarray*} \ begin {aligned} \ begin {cases}-ΔU+λu= f（u）\ \ {\ rm in} \ int _ {\ Mathbb {r}^2} u^2dx =ρ，\ end {cases} \ end {aligned} \ end {eqnarray*}，其中给出了$ρ> 0 $，$λ\ in $ mathbb {r} $ aist a lagrange multial and lagrange multiff $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f。在不假设Ambrosetti-Rabinowitz条件下，我们显示了任何$ρ> 0 $的归一化基态解决方案。该证明基于$ \ mathbb {r}^2 $中的约束最小化方法和Trudinger-Moser不等式。
We are concerned with the following nonlinear Schrödinger equation \begin{eqnarray*} \begin{aligned} \begin{cases} -Δu+λu=f(u) \ \ {\rm in}\ \mathbb{R}^{2},\\ u\in H^{1}(\mathbb{R}^{2}),~~~ \int_{\mathbb{R}^2}u^2dx=ρ, \end{cases} \end{aligned} \end{eqnarray*} where $ρ>0$ is given, $λ\in\mathbb{R}$ arises as a Lagrange multiplier and $f$ satisfies an exponential critical growth. Without assuming the Ambrosetti-Rabinowitz condition, we show the existence of normalized ground state solutions for any $ρ>0$. The proof is based on a constrained minimization method and the Trudinger-Moser inequality in $\mathbb{R}^2$.
