1. Universal Bounds for Eigenvalues of a Buckling Problem
- Author
-
Hongcang Yang and Qing-Ming Cheng
- Subjects
Buckling ,Euclidean space ,Bounded function ,Complex system ,Biharmonic equation ,Applied mathematics ,Statistical and Nonlinear Physics ,Mathematics::Spectral Theory ,Mathematical Physics ,Domain (mathematical analysis) ,Eigenvalues and eigenvectors ,Mathematics ,Bounded operator - Abstract
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, Polya and Weinberger in [14] and this problem has been mentioned again by Ashbaugh in [1].
- Published
- 2005
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