Czechoslovak Mathematical Journal, Vol. 69, No. 2, pp. 485-501, 2019


On the spectrum of Robin Laplacian in a planar waveguide

Alex Ferreira Rossini

Received August 25, 2017.   Published online October 22, 2018.

Abstract:  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.
Keywords:  planar waveguide; discrete spectrum; Robin boundary conditions
Classification MSC:  47B25, 47F05, 49R05, 81Q10
DOI:  10.21136/CMJ.2018.0396-17


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Affiliations:   Alex Ferreira Rossini, Instituto de Matemática, Universidade Federal de Mato Grosso do Sul, Cidade Universitária, s/n, Avenida Costa e Silva, 79070-900, Campo Grande, Brazil, e-mail: alex.rossini@ufms.br


 
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