Second eigenvalue of the Yamabe operator and applications

被引：18

作者：

El Sayed, S. ^{[1
]}

机构：

[1] Univ Tours, Lab Math & Phys Theor, F-37200 Tours, France

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2014年 / 50卷 / 3-4期

关键词：

COMPACT RIEMANNIAN-MANIFOLDS; NONLINEAR ELLIPTIC-EQUATIONS; SCALAR CURVATURE; NODAL SOLUTIONS; INVARIANT;

D O I：

10.1007/s00526-013-0651-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (M, g) be a compact Riemannian manifold of dimension n >= 3 . In this paper, we give various properties of the eigenvalues of the Yamabe operator . In particular, we show how the second eigenvalue of L-g is related to the existence of nodal solutions of the equation L-g(u) =epsilon vertical bar u vertical bar(N-2)u, where epsilon = +1, 0, or -1.

引用

页码：665 / 692

页数：28

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