Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (2): 545-550.doi: 10.1007/s10473-019-0217-3

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NEW BOUNDS ON EIGENVUALUES OF LAPLACIAN

Zhengchao JI   

  1. Center of Mathematical Scienses, Zhejiang University, Hangzhou 310027, China
  • Received:2018-01-07 Revised:2018-08-01 Online:2019-04-25 Published:2019-05-06

Abstract: In this paper, we investigate non-zero positive eigenvalues of the Laplacian with Dirichlet boundary condition in an n-dimentional Euclidean space Rn, then we obtain an new upper bound of the (k + 1)-th eigenvalue λk+1, which improve the previous estimate which was obtained by Cheng and Yang, see (1.8).

Key words: eigenvalues, Laplacian, Euclidean space, recursion formula

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