论文标题
处方$ Q $ -CURVATURES问题的紧凑性和存在结果$ \ Mathbb {s}^n $
Compactness and existence results of the prescribing fractional $Q$-curvatures problem on $\mathbb{S}^n$
论文作者
论文摘要
This paper is devoted to establishing the compactness and existence results of the solutions to the prescribing fractional $Q$-curvatures problem of order $2σ$ on $n$-dimensional standard sphere when $ n-2σ=2$, $σ=1+m/2,$ $m\in \mathbb{N}_{+}.$ The compactness results are novel and optimal.此外，我们证明了所有解决方案的学位公式，以实现存在。从我们的结果来看，我们可以知道发生爆炸的地方。此外，可以构建在任何有限的不同位置上精确炸毁的解决方案的序列。值得注意的是，我们的结果包括多个谐波的情况。
This paper is devoted to establishing the compactness and existence results of the solutions to the prescribing fractional $Q$-curvatures problem of order $2σ$ on $n$-dimensional standard sphere when $ n-2σ=2$, $σ=1+m/2,$ $m\in \mathbb{N}_{+}.$ The compactness results are novel and optimal. In addition, we prove a degree-counting formula of all solutions to achieve the existence. From our results, we can know where blow up occur. Furthermore, the sequence of solutions that blow up precisely at any finite distinct location can be constructed. It is worth noting that our results include the case of multiple harmonic.
