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UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR OF ANY ORDER 被引量:7

UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR OF ANY ORDER
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摘要 Let Ω be a connected bounded domain in R^n. Denote by λi the i-th eigenvalue of the Lapla^ian operator with any order p:{u=Эn→^-Эu=…=Эn→p-1^-Эp-1u=0 on ЭΩ (-△)pu=λu in Ω.In this article, we give some expressions for upper bound of the (k + 1)-th eigenvalue )λk+l in terms of the first k eigenvalues. Let Ω be a connected bounded domain in R^n. Denote by λi the i-th eigenvalue of the Lapla^ian operator with any order p:{u=Эn→^-Эu=…=Эn→p-1^-Эp-1u=0 on ЭΩ (-△)pu=λu in Ω.In this article, we give some expressions for upper bound of the (k + 1)-th eigenvalue )λk+l in terms of the first k eigenvalues.
出处 《Acta Mathematica Scientia》 SCIE CSCD 2010年第3期939-948,共10页 数学物理学报(B辑英文版)
基金 supported by NSFC (10471108,10631020) of China NSF of Henan Provincial Education Department (2010A110008)
关键词 EIGENVALUE Laplacian operator Eigenvalue Laplacian operator
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