Applications of the ‘Ham Sandwich Theorem’ to Eigenvalues of the Laplacian

Kei Funano

Displaying similar documents to “Applications of the ‘Ham Sandwich Theorem’ to Eigenvalues of the Laplacian”

An integro-differential inequality related to the smallest positive eigenvalue ofp(x)-Laplacian Dirichlet problem

Damian Wiśniewski, Mariusz Bodzioch (2016)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.

On some properties of eigenvalues and eigenfunctions of certain differential equations of the fourth order

Jan Bochenek (1971)

Annales Polonici Mathematici

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About a Pólya-Schiffer inequality

Bodo Dittmar, Maren Hantke (2011)

Annales UMCS, Mathematica

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For simply connected planar domains with the maximal conformal radius 1 it was proven in 1954 by G. Pólya and M. Schiffer that for the eigenvalues λ of the fixed membrane for any n the following inequality holds [...] where λ(o) are the eigenvalues of the unit disk. The aim of the paper is to give a sharper version of this inequality and for the sum of all reciprocals to derive formulas which allow in some cases to calculate exactly this sum.

Equality in Wielandt’s eigenvalue inequality

Shmuel Friedland (2015)

Special Matrices

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In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.

Inequalities among eigenvalues of Sturm-Liouville problems.

Eastham, M.S.P., Kong, Q., Wu, H., Zettl, A. (1999)

Journal of Inequalities and Applications [electronic only]

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On the Approximative Construction of the Eigenvectors Corresponding to a Pair of Complex Conjugated Eigenvalues

Ivo Marek (1964)

Matematicko-fyzikálny časopis

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On eigenvalues and eigenfunctions of an operational equation

Jan Bochenek (1971)

Annales Polonici Mathematici

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Dependence of a differential equation on the first eigenvalue of a suitable problem

Jan Bochenek (1980)

Annales Polonici Mathematici

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On the lowest eigenvalue of the Laplacian for the intersection of two domains.

Elliott H. Lieb (1983)

Inventiones mathematicae

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Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems

J. Fleckinger, J. Hernández, F. Thélin (2004)

Bollettino dell'Unione Matematica Italiana

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We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.

Open set of eigenvalues and SVEP

J. Bračič, V. Müller (2007)

Banach Center Publications

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Extension of Díaz-Saá's inequality in R and application to a system of p-Laplacian.

Karim Chaïb (2002)

Publicacions Matemàtiques

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The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as R^N. The proof is based on the Picone’s identity which is very useful in problems involving p-Laplacian. In a second part, we study some properties of the first eigenvalue for a system of p-Laplacian. We use Díaz-Saá’s inequality to prove uniqueness and Egorov’s theorem for the isolation. These results generalize J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis...