论文标题
一些非均匀的gagliardo-nirenberg不平等现象，并应用于Biharmonic非线性Schrödinger方程
Some non-homogeneous Gagliardo-Nirenberg inequalities and application to a biharmonic non-linear Schrödinger equation
论文作者
论文摘要
我们研究了具有混合色散的四阶schrödinger方程的常规波，当$ l^2- $ norm（\ textit {mass}）}时，将相关能量最小化。我们需要一些非均匀的gagliardo-nirenberg型不平等，我们开发了一种证明在其他地方应该有用的估计值的方法。我们证明了在{\ it subsubcilitical}和{\ it质量批判性}情况下的最小化情况的最佳结果。在{\ IT质量超临界}情况下，我们表明全局最小化不存在，我们研究了局部最小化器的存在。如果质量不超过（0，+\ infty）$ in（0，+\ infty）$的某些阈值$μ_0\，则我们在“最佳”本地最小化器上的结果也是最佳的。
We study the standing waves for a fourth-order Schrödinger equation with mixed dispersion that minimize the associated energy when the $L^2-$norm (the \textit{mass}) } is kept fixed. We need some non-homogeneous Gagliardo-Nirenberg-type inequalities and we develop a method to prove such estimates that should be useful elsewhere. We prove optimal results on the existence of minimizers in the {\it mass-subcritical } and {\it mass-critical } cases. In the { \it mass supercritical} case we show that global minimizers do not exist, and we investigate the existence of local minimizers. If the mass does not exceed some threshold $ μ_0 \in (0,+\infty)$, our results on "best" local minimizers are also optimal.
