A global result for discrete ϕ-Laplacian eigenvalue problems
نویسندگان
چکیده
منابع مشابه
A Global Curvature Pinching Result of the First Eigenvalue of the Laplacian on Riemannian Manifolds
and Applied Analysis 3 then there exists a constant C 3 (n) > 0 such that λ 1 (M) ≥ C 3 (n). Proof. The proof mainly belongs to Li and Yau [6]. Let u be the normalized eigenfunction ofM, set V = log (a + u) where a > 1. Then, we can easily get that ΔV = −λ 1 (M) u a + u − |∇V| 2 . (8) Denote that Q(x) = |∇V|(x), and we then have by the Ricci identity on manifolds with Ric (M) ≥ 0:
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2013
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2013-264