论文标题
Yamabe型方程的局部分叉图和退化解决方案
Local bifurcation diagrams and degenerate solutions of Yamabe-type equations
论文作者
论文摘要
我们研究方程式的阳性解决方案$-Δ_Gu +λu=λu^q $，$λ> 0 $，$ q> 1 $在圆形球体上$ \ mathbb {s}^n $。我们通过考虑等化函数并采用分叉理论来将方程式减少到普通的微分方程。我们研究相应的分叉点何时是跨危。我们将此结果应用于方程式显示退化溶液的存在，并研究了保形恒定标量曲率指标的多重性结果。
We study positive solutions of the equation $-Δ_g u + λu = λu^q$, with $λ>0$, $q>1$ on the round sphere $\mathbb{S}^n$ . We reduce the equation to an ordinary differential equation by considering isoparametric functions and apply bifurcation theory. We study when the corresponding bifurcation points are transcritical. We apply this result to show the existence of degenerate solutions to the equation and to study multiplicity results for conformal constant scalar curvature metrics.
