Abstract Let ( M , g ) be a smooth and compact Riemannian manifold with dimensions n ≥ 3 . This paper deals with the existence of nontrivial solutions for a nonlinear second-order elliptic equation with a singular term and critical Sobolev growth. We provide a geometric application of this singular equation.

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关于奇异二阶椭圆方程

摘要 令( M , g ) 是一个光滑紧凑的黎曼流形，维度n ≥ 3。本文讨论了具有奇异项和临界 Sobolev 增长的非线性二阶椭圆方程的非平凡解的存在性。我们提供了这个奇异方程的几何应用。