论文标题
Sobolev CriticalSchrödinger方程的基态轨道稳定性
Orbital stability of ground states for a Sobolev critical Schrödinger equation
论文作者
论文摘要
我们研究了具有混合功率非线性的非线性schrödinger方程的基态立场，处方质量的存在\ begin {方程*} i \ partial_t v +Δv +μv| v |^{q -2} + v | v |^{2^* - 2} = 0，\ quad（t，x）\ in \ sathbb {r} \end{equation*} where $N \geq 3$, $v: \mathbb{R} \times \mathbb{R}^N \to \mathbb{C}$, $μ> 0$, $2 < q < 2 + 4/N $ and $2^* = 2N/(N-2)$ is the critical Sobolev exponent.我们表明，所有基态都对应于相关能量功能的局部最小值。接下来，尽管非线性是Sobolev批判性的事实，但我们证明了基础状态的集合是轨道稳定的。我们的结果解决了N. Soave [35]提出的问题。
We study the existence of ground state standing waves, of prescribed mass, for the nonlinear Schrödinger equation with mixed power nonlinearities \begin{equation*} i \partial_t v + Δv + μv |v|^{q-2} + v |v|^{2^* - 2} = 0, \quad (t, x) \in \mathbb{R} \times \mathbb{R}^N, \end{equation*} where $N \geq 3$, $v: \mathbb{R} \times \mathbb{R}^N \to \mathbb{C}$, $μ> 0$, $2 < q < 2 + 4/N $ and $2^* = 2N/(N-2)$ is the critical Sobolev exponent. We show that all ground states correspond to local minima of the associated Energy functional. Next, despite the fact that the nonlinearity is Sobolev critical, we show that the set of ground states is orbitally stable. Our results settle a question raised by N. Soave [35].
