Universal Bounds for Eigenvalues of a Buckling Problem
Qing-Ming Cheng,Hongcang Yang +1 more
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In this paper, a new method to construct ''nice'' trial functions was introduced and a universal inequality for higher eigenvalues of the buckling problem was derived by making use of the trial functions.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].read more
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Universal Inequalities for Eigenvalues of the Buckling Problem of Arbitrary Order
TL;DR: In this paper, the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres were investigated and universal bounds for the $k$th eigenvalue in terms of the lower eigen values independently of the particular geometry of the domain were obtained.
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Eigenvalues of the buckling problem of arbitrary order on bounded domains of $\mathbb{M}\times\mathbb{R}$
Qiaoling Wand,Changyu Xia +1 more
TL;DR: In this article, the authors obtained universal inequalities for eigenvalues of the buckling problem of arbitrary order on bounded domains in O(n) space in the dimension of the domain, where n is the number of vertices in the domain.
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Inequalities for the navier and dirichlet eigenvalues of elliptic operators
Qiaoling Wang,Changyu Xia +1 more
TL;DR: In this article, the eigenvalues of elliptic operators on a bounded domain in a Euclidean space were studied and lower bounds were obtained for higher order operators of higher orders with Navier boundary condition.
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On the spectral asymptotics for the buckling problem
TL;DR: In this article, the buckling eigenvalues of the biharmonic operator on domains of Rd of finite measure were shown to be bounded by the so-called "averaged variational principle".
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Estimates on the first two poly-laplacian eigenvalues on spherical domains
TL;DR: In this paper, the first two eigenvalues of the higher-order buckling problem on a domain in the unit sphere were studied and an estimate on the second eigenvalue in terms of the first eigen value was obtained.
References
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Journal ArticleDOI
On the ratio of consecutive eigenvalues
Journal ArticleDOI
On trace identities and universal eigenvalue estimates for some partial differential operators
Evans M. Harrell,Joachim Stubbe +1 more
TL;DR: In this paper, a trace identity for the spectra of self-adjoint operators H modeled on the Dirichlet Laplacian or, more generally, on Schrodinger operators of the form (p−A(x))2 + V (x), where p = 1i ∇ is the usual momentum operator in convenient units and A(x) is the magnetic vector potential.
Journal ArticleDOI
Estimates on Eigenvalues of Laplacian
Qing-Ming Cheng,Hongcang Yang +1 more
TL;DR: In this article, the eigenvalues of Laplacian on a bounded connected domain in an n-dimensional unit sphere Sn(1) or a compact homogeneous Riemannian manifold were studied.
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Inequalities for eigenvalues of a clamped plate problem
Qing-Ming Cheng,Hongcang Yang +1 more
TL;DR: In this article, an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues, which is independent of the domain D, is obtained.
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