Applicable Analysis and Discrete Mathematics 2022 Volume 16, Issue 2, Pages: 534-547
https://doi.org/10.2298/AADM220323036B
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A q-Dirac boundary value problem with eigenparameter-dependent boundary conditions
Bohner Martin (Missouri University of Science and Technology, Rolla, USA), bohner@mst.edu
Çetinkaya Ayça (Department of Mathematics, Mersin University, Mersin, Turkey), faycacetinkaya@mersin.edu.tr
We study a boundary value problem for the q-Dirac equation and
eigenvalue-dependent boundary conditions. We introduce a self-adjoint
operator in a suitable Hilbert space and illustrate the boundary value
problem as a spectral problem for this operator. We investigate the
properties of the eigenvalues and vector-valued eigenfunctions. We construct
Green’s function.
Keywords: q-calculus, Dirac operator, Boundary value problems, Eigenvalues and eigenfunctions, Green’s function
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