Eigenvalues of the buckling problem of arbitrary order and of the polyharmonic operator on Ricci flat manifolds

被引：7
作者：
Du, Feng [1 ,2 ]
Wu, Chuanxi [1 ]
Li, Guanghan [1 ]
Xia, Changyu [1 ,3 ]
机构：
[1] Hubei Univ, Sch Math & Stat, Wuhan 430062, Peoples R China
[2] Jingchu Univ Technol, Sch Math & Phys Sci, Jingmen 448000, Peoples R China
[3] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 417卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Eigenvalues; Universal bounds; Ricci flat manifold; Buckling problem; Polyharmonic operator; UNIVERSAL BOUNDS; INEQUALITIES; LAPLACIAN;
D O I：
10.1016/j.jmaa.2014.03.050
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study eigenvalues of the buckling problem of arbitrary order and of the polyharmonic operator on bounded domains in Ricci flat manifolds supporting a special function and obtain universal bounds on the (k + 1)th eigenvalue in terms of the first k eigenvalues independent of the domains. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：601 / 621
页数：21
相关论文
共 11 条
  • [1] Chen Z-C., 1990, J. China Univ. Sci. Tech, V20, P259
  • [2] UNIVERSAL BOUNDS FOR EIGENVALUES OF A BUCKLING PROBLEM II
    Cheng, Qing-Ming
    Yang, Hongcang
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (11) : 6139 - 6158
  • [3] INEQUALITIES FOR EIGENVALUES OF LAPLACIAN WITH ANY ORDER
    Cheng, Qing-Ming
    Ichikawa, Takamichi
    Mametsuka, Shinji
    [J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2009, 11 (04) : 639 - 655
  • [4] Universal bounds for eigenvalues of a buckling problem
    Cheng, QM
    Yang, HC
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 262 (03) : 663 - 675
  • [5] CHENG QM, PREPRINT
  • [6] Hardy G., 1994, INEQUALITY, V2nd
  • [7] Huang GY, 2010, ACTA MATH SCI, V30, P939
  • [8] UNIVERSAL BOUNDS FOR EIGENVALUES OF THE POLYHARMONIC OPERATORS
    Jost, Juergen
    Li-Jost, Xianqing
    Wang, Qiaoling
    Xia, Changyu
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (04) : 1821 - 1854
  • [9] Universal Inequalities for Eigenvalues of the Buckling Problem of Arbitrary Order
    Jost, Juergen
    Li-Jost, Xianqing
    Wang, Qiaoling
    Xia, Changyu
    [J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (09) : 1563 - 1589
  • [10] Universal inequalities for eigenvalues of the buckling problem on spherical domains
    Wang, Qiaoling
    Xia, Changyu
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 270 (03) : 759 - 775
12