论文标题
无限的许多起泡解决方案和非分数的曲率问题结果
Infinitely many bubbling solutions and non-degeneracy results to fractional prescribed curvature problems
论文作者
论文摘要
我们考虑以下分数处方曲率问题$$（-Δ）^s u = k（y） $ s \ in（0,1）$ for $ n \ geqslant4 $和$ 2^*_ s = \ frac {2n} {n-2s} $是分数的关键sobolev endents，$ k（y）$具有$ r \ in（r_0-Δ，r_0-Δ，r_0+δ）$r_0-Δ，r_0+δ）的本地最大点。首先，对于任何足够大的$ k $，我们将$ 2K的$冒泡解决方案构建为（0.1）的某些新型，该解决方案集中在通过Lyapunov-Schmidt减少方法上的磨碎圆柱体的上和下表面上。此外，通过使用各种Pohozaev身份证明了多润滑溶液的非分类结果，这在分数问题的研究中是新的。
We consider the following fractional prescribed curvature problem $$(-Δ)^s u= K(y)u^{2^*_s-1},\ \ u>0,\ \ y\in \mathbb{R}^N,\qquad (0.1)$$ where $s\in(0,\frac{1}{2})$ for $N=3$, $s\in(0,1)$ for $N\geqslant4$ and $2^*_s=\frac{2N}{N-2s}$ is the fractional critical Sobolev exponent, $K(y)$ has a local maximum point in $r\in(r_0-δ,r_0+δ)$. First, for any sufficient large $k$, we construct a $2k$ bubbling solution to (0.1) of some new type, which concentrate on an upper and lower surfaces of an oblate cylinder through the Lyapunov-Schmidt reduction method. Furthermore, a non-degeneracy result of the multi-bubbling solutions is proved by use of various Pohozaev identities, which is new in the study of the fractional problems.
