论文标题
Yamabe型方程的淋巴结溶液在阳性RICCI曲率歧管上
Nodal solutions of Yamabe-type equations on positive Ricci curvature manifolds
论文作者
论文摘要
我们考虑了一个封闭的同构性一个riemannian歧管$（m^n，g）$ dimension $ n \ geq 3 $。如果$ m $的RICCI曲率为正，我们证明存在$-Δ_Gu +λu=λu=λu^q $的无限节点解决方案，$λ> 0 $，$ q>> 1 $。特别是对于一个共同体的阳性爱因斯坦歧管，或者在同时植物上具有纤维，一个爱因斯坦歧管上的爱因斯坦歧管，我们证明了yamabe方程中的无限节点溶液的存在，并具有规定的其节点结构域的相互连接的组件。
We consider a closed cohomogeneity one Riemannian manifold $(M^n,g) $ of dimension $n\geq 3$. If the Ricci curvature of $M$ is positive, we prove the existence of infinite nodal solutions for equations of the form $-Δ_g u + λu = λu^q$ with $λ>0$, $q>1$. In particular for a positive Einstein manifold which is of cohomogeneity one or fibers over a cohomogeniety one Einstein manifold we prove the existence of infinite nodal solutions for the Yamabe equation, with a prescribed number of connected components of its nodal domain.
