On a class of operators
V. Rakočević (1985)
Matematički Vesnik
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V. Rakočević (1985)
Matematički Vesnik
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S. Naboko (1993-1994)
Séminaire Équations aux dérivées partielles (Polytechnique)
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Jakubassa-Amundsen, D.H. (2002)
Mathematical Physics Electronic Journal [electronic only]
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Jean Dolbeault, Maria Esteban, Eric Séré (2006)
Journal of the European Mathematical Society
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This paper is concerned with an extension and reinterpretation of previous results on the variational characterization of eigenvalues in gaps of the essential spectrum of self-adjoint operators. We state two general abstract results on the existence of eigenvalues in the gap and a continuation principle. Then these results are applied to Dirac operators in order to characterize simultaneously eigenvalues corresponding to electronic and positronic bound states.
Maksudov, F.G. (1997)
Memoirs on Differential Equations and Mathematical Physics
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Yu. Abramov (1977)
Studia Mathematica
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Albert Schneider, Frank Mantlik (1990)
Mathematische Zeitschrift
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Neuberger, J.W., Renka, R.J. (1999)
Experimental Mathematics
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Pavel Drábek (2014)
Mathematica Bohemica
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General mathematical theories usually originate from the investigation of particular problems and notions which could not be handled by available tools and methods. The Fučík spectrum and the -Laplacian are typical examples in the field of nonlinear analysis. The systematic study of these notions during the last four decades led to several interesting and surprising results and revealed deep relationship between the linear and the nonlinear structures. This paper does not provide a...
Mikhail Sh. Birman (1994)
Journées équations aux dérivées partielles
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Alex Ferreira Rossini (2019)
Czechoslovak Mathematical Journal
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We consider the Laplace operator in a planar waveguide, i.e. an infinite two-dimensional straight strip of constant width, with Robin boundary conditions. We study the essential spectrum of the corresponding Laplacian when the boundary coupling function has a limit at infinity. Furthermore, we derive sufficient conditions for the existence of discrete spectrum.