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Universal Bounds for Eigenvalues of a Buckling Problem

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In this paper, we investigate an eigenvalue problem for a biharmonic operator on a bounded domain in an n-dimensional Euclidean space, which is also called a buckling problem. We introduce a new method to construct ``nice'' trial functions and we derive a universal inequality for higher eigenvalues of the buckling problem by making use of the trial functions. Thus, we give an affirmative answer for the problem on universal bounds for eigenvalues of the buckling problem, which was proposed by Payne, Pólya and Weinberger in [14] and this problem has been mentioned again by Ashbaugh in [1].

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Correspondence to Qing-Ming Cheng.

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Communicated by B. Simon

Research partially supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science.

Research partially supported by SF of CAS

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Cheng, QM., Yang, H. Universal Bounds for Eigenvalues of a Buckling Problem. Commun. Math. Phys. 262, 663–675 (2006).

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