In this article, we consider the eigenvalue problem for the bi-Kohn Laplacian and obtain universal bounds on the （k ＋ 1）-th eigenvalue in terms of the first k eigenvalues independent of the domains.
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 som...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.展开更多
In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the （k ＋ 1）th eigenvalue in terms of the first kth eigenvalues in...In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the （k ＋ 1）th eigenvalue in terms of the first kth eigenvalues independent of the domains.展开更多
基金Supported by National Natural Science Foundation of China (1100107610926171+4 种基金10926172)Project of Henan Provincial Department of Sciences and Technology (092300410143)NSF of Henan Provincial Education Department (2009A1100102010A110008)Foundation of Young Backbone Teachers of Henan Normal University
基金Supported by National Natural Science Foundation of China(1100107610926171+4 种基金10926172)Project of Henan Provincial Department of Sciences and Technology(092300410143)NSF of Henan Provincial Education Department(2009A1100102010A110008)Foundation of Young Backbone Teachers of Henan Normal University
基金Supported by NSFC of China (No.10671181)Project of Henan Provincialdepart ment of Sciences and Technology (No.092300410143)NSF of Henan Provincial Education depart ment (No .2009A110010)
文摘In this article, we consider the eigenvalue problem for the bi-Kohn Laplacian and obtain universal bounds on the （k ＋ 1）-th eigenvalue in terms of the first k eigenvalues independent of the domains.
基金supported by NSFC (10471108,10631020) of ChinaNSF of Henan Provincial Education Department (2010A110008)
文摘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.
基金supported by NSFC (11001076)Project of Henan Provincial department of Sciences and Technology (092300410143)+1 种基金NSF of Henan Provincial Education Department (2009A110010 2010A110008)
文摘In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the （k ＋ 1）th eigenvalue in terms of the first kth eigenvalues independent of the domains.
