文献类型：期刊文献

英文题名：Dimension-like functions and nonlinear spectrums of Finsler manifolds

作者：Shen, Zhongmin[1]; Zhao, Wei[2]

机构：[1] Department of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, IN, United States; [2] Department of Mathematics, East China University of Science and Technology, Shanghai, China

年份：2018

外文期刊名：arXiv

收录：EI(收录号：20200038482)

语种：英文

外文关键词：Boundary value problems - Sobolev spaces

摘要：In this paper, we study the spectral problem on a compact Finsler manifold with or without boundary. More precisely, given a certain collection of sets in Sobolev space H1,2(M) and a dimension-like function, we can define a corresponding spectrum. Such a spectrum satisfies nice properties. In particular, the eigenfunction corresponding to each eigenvalue always exists. And a Cheng type upper bound estimate for eigenvalues is obtained. Moreover, some interesting examples are constructed and investigated in this paper. Copyright ? 2018, The Authors. All rights reserved.