论文标题
在$ {\ mathbb {s}}}^n $上为规定的标量曲率问题加倍赤道
Doubling the equatorial for the prescribed scalar curvature problem on ${\mathbb{S}}^N$
论文作者
论文摘要
我们考虑$ {\ MathBb {s}}^n $ $ $ $ $δ_{{{\ MathBB s}^n} v- \ frac {n（n-2）} {2} v+tilde {v+tilde {k}（k}（k}（y） \ mbox {on} \ {\ Mathbb s}^n，\ qquad v> 0 \ quad \ mbox {on} \ {\ mathbb s}^n，$ $在标量曲率$ \ tilde k $旋转的polotational symetres symets symettres and poles之间的假设下，$ $。我们证明了无限的许多非主阳性解决方案的存在，它们的能量可以任意大。这些解决方案在$ O（3）$的某些非平地子组下是不变的，使赤道增加了一倍。我们使用有限的尺寸Lyapunov-Schmidt还原方法。
We consider the prescribed scalar curvature problem on $ {\mathbb{S}}^N $ $$ Δ_{{\mathbb S}^N} v-\frac{N(N-2)}{2} v+\tilde{K}(y) v^{\frac{N+2}{N-2}}=0 \quad \mbox{on} \ {\mathbb S}^N, \qquad v >0 \quad \mbox{on} \ {\mathbb S}^N, $$ under the assumptions that the scalar curvature $\tilde K$ is rotationally symmetric, and has a positive local maximum point between the poles. We prove the existence of infinitely many non-radial positive solutions, whose energy can be made arbitrarily large. These solutions are invariant under some non-trivial sub-group of $O(3)$ obtained doubling the equatorial. We use the finite dimensional Lyapunov-Schmidt reduction method.
