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The Algebraic Multiplicity of Eigenvalues and the Evans Function Revisited

Y. Latushkin, A. Sukhtayev (2010)

Mathematical Modelling of Natural Phenomena

This paper is related to the spectral stability of traveling wave solutions of partial differential equations. In the first part of the paper we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an abstract operator on a Hilbert space, and the algebraic multiplicity of the eigenvalue of the corresponding Birman-Schwinger type operator pencil. In the second part of the paper we apply this result...

The Allegretto-Piepenbrink theorem for strongly local Dirichlet forms.

Lenz, Daniel, Stollmann, Peter, Veselić, Ivan (2009)

Documenta Mathematica

The Essential Spectrum of Elliptic Systems of Mixed Order.

Gerd Grubb, Giuseppe Geymonat (1977)

Mathematische Annalen

The essential spectrum of relativistic one-electron ions in the Jansen-Hess model.

Jakubassa-Amundsen, D.H. (2002)

Mathematical Physics Electronic Journal [electronic only]

The first eigenvalue of $p$ -Laplacian systems with nonlinear boundary conditions.

Kandilakis, D.A., Magiropoulos, M., Zographopoulos, N.B. (2005)

Boundary Value Problems [electronic only]

The generalized Morawetz problem for Lavrent'ev-Bitsadze equation with spectral parameter.

Shustrova, N.V. (2006)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

The Laplace-Beltrami operator in almost-Riemannian Geometry

Ugo Boscain, Camille Laurent (2013)

Annales de l’institut Fourier

We study the Laplace-Beltrami operator of generalized Riemannian structures on orientable surfaces for which a local orthonormal frame is given by a pair of vector fields that can become collinear.Under the assumption that the structure is 2-step Lie bracket generating, we prove that the Laplace-Beltrami operator is essentially self-adjoint and has discrete spectrum. As a consequence, a quantum particle cannot cross the singular set (i.e., the set where the vector fields become collinear) and the...

The linear symmetric systems associated with the modified Cherednik operators and applications

Hatem Mejjaoli (2012)

Annales mathématiques Blaise Pascal

We introduce and study the linear symmetric systems associated with the modified Cherednik operators. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite propagation speed property of it.

The optimal shape of a dendrite sealed at both ends

Yannick Privat (2009)

Annales de l'I.H.P. Analyse non linéaire

The Schrödinger equation on non-stationary domains.

Karner, Gunther (1998)

Electronic Journal of Differential Equations (EJDE) [electronic only]

The second eigenvalue of the $p$ -Laplacian as $p$ goes to 1.

Parini, Enea (2010)

International Journal of Differential Equations

The simplified Wheeler-Dewitt equation : the Cauchy problem and some spectral properties

João-Paulo Dias, Mário Figueira (1991)

Annales de l'I.H.P. Physique théorique

The sine-cosine method for the Davey-Stewartson equations.

Zedan, Hassan A., Monaquel, Shatha Jameel (2010)

Applied Mathematics E-Notes [electronic only]

The spectral cutting problem

M. Burnat (1982)

Banach Center Publications

The spectral properties of the Schrödinger operator in nonseparable Hilbert spaces

M. Burnat (1982)

Banach Center Publications

The Spectrum of the Continuous Laplacian on a Graph.

Carla Cattaneo (1997)

Monatshefte für Mathematik

The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent

Yannick Privat, Mario Sigalotti (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of...

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