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.
Shmuel Friedland (2015)
Special Matrices
Similarity:
In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.
Julián Fernández Bonder, Julio D. Rossi (2002)
Publicacions Matemàtiques
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In this paper we study the Sobolev trace embedding W(Ω) → L (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λ / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end...
A. G. Ramm (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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The main results of this paper are: 1) a proof that a necessary condition for 1 to be an eigenvalue of the S-matrix is real analyticity of the boundary of the obstacle, 2) a short proof that if 1 is an eigenvalue of the S-matrix, then k² is an eigenvalue of the Laplacian of the interior problem, and that in this case there exists a solution to the interior Dirichlet problem for the Laplacian, which admits an analytic continuation to the whole space ℝ³ as an entire function.
Kei Funano (2016)
Analysis and Geometry in Metric Spaces
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We apply Gromov’s ham sandwich method to get: (1) domain monotonicity (up to a multiplicative constant factor); (2) reverse domain monotonicity (up to a multiplicative constant factor); and (3) universal inequalities for Neumann eigenvalues of the Laplacian on bounded convex domains in Euclidean space.
Jan Bochenek (1980)
Annales Polonici Mathematici
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Benedikt, Jiří (2004)
Abstract and Applied Analysis
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Gossez, Jean-Pierre, Lami Dozo, Enrique (1982)
Portugaliae mathematica
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Denis Borisov, Giuseppe Cardone (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We show that this two-parametric set contains any prescribed number of the first eigenvalues of the considered operator. We obtain the complete asymptotic expansions for the eigenfunctions...
Behrouz Emamizadeh, Amin Farjudian (2014)
Nonautonomous Dynamical Systems
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In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will...
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.
Jan Bochenek (1971)
Annales Polonici Mathematici
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Elliott H. Lieb (1983)
Inventiones mathematicae
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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 RN. 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...