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
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: firstname.lastname@example.org