Second eigenvalue of the Yamabe operator and applications

被引：17
|
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.
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页码：665 / 692
页数：28
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