New Bounds on Eigenvualues of Laplacian
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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 wordseigenvalues Laplacian Euclidean space recursion formula
2010 MR Subject Classification35P15 58G25
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The author would like to thank Professor Kefeng Liu and Professor Hongwei Xu for their continued support, advice and encouragement. Thanks also to Professor En-Tao Zhao for helpful discussions.
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