论文标题
具有一般Sobolev关键非线性的非线性Schrödinger方程的归一化基态
Normalized ground states for nonlinear Schrödinger equations with general Sobolev critical nonlinearities
论文作者
论文摘要
在本文中，我们研究了以下非线性schrödinger方程的归一化解决方案的存在\ begin {equation*} \ left {\ oken {aligned}＆-Δu= f（u）+λu\λu\ quad \ quad \ quad \ quad \ quad \ quad \ mbox {in} h^1（\ mathbb {r}^n），~~~ \ int _ {\ mathbb {r}^n} | u | u |^2dx = c，\ end end {aligned} \ right。 \ end {equation*}其中$ n \ ge3 $，$ c> 0 $，$λ\ in \ mathbb {r} $ and $ f $在无穷大时具有sobolev的临界增长，但不满足Ambrosetti-Rabinowitz条件。通过分析基态能源相对于$ c $的单调性，我们开发了一种有限的最小化方法，以确定所有$ c> 0 $的归一化基态解决方案的存在。
In this paper, we study the existence of normalized solutions to the following nonlinear Schrödinger equation \begin{equation*} \left\{ \begin{aligned} &-Δu=f(u)+ λu\quad \mbox{in}\ \mathbb{R}^{N},\\ &u\in H^1(\mathbb{R}^N), ~~~\int_{\mathbb{R}^N}|u|^2dx=c, \end{aligned} \right. \end{equation*} where $N\ge3$, $c>0$, $λ\in \mathbb{R}$ and $f$ has a Sobolev critical growth at infinity but does not satisfies the Ambrosetti-Rabinowitz condition. By analysing the monotonicity of the ground state energy with respect to $c$, we develop a constrained minimization approach to establish the existence of normalized ground state solutions for all $c>0$.
