Geodesic
On Dirac systems with multi-eigenparameter-dependent transmission conditions
Filomat, Tome 36 (2022) no. 10, p. 3355

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DOI

In this work, we investigate a Dirac system which has discontinuities at finite interior points and contains eigenparameter in both boundary and transmission conditions. By defining a suitable Hilbert space H associated with the problem, we generate a self-adjoint operator T such that the eigenvalues of the considered problem coincide with those of T . We construct the fundamental system of solutions of the problem and get the asymptotic formulas for the fundamental solutions, eigenvalues and eigen-vector- functions. Also, we examine the asymptotic behaviour for the norm of eigenvectors corresponding to the operator T . We construct Green’s matrix, and derive the resolvent of the operator T in terms of Green’s matrix. Finally, we estimate the norm of resolvent of the operator T . In the special case, when our problem has no eigenparameter in both boundary and transmission conditions, the obtained results coincide with the corresponding results in Tharwat (Boundary Value Problems, DOI:10.1186/s13661-015-0515-1, 2016).
DOI : 10.2298/FIL2210355T
Classification : 34B08, 34B27, 34L20
Keywords: Dirac systems, transmission conditions, discontinuous boundary value problems, Green’s matrix, resolvent operator 
M M Tharwat. On Dirac systems with multi-eigenparameter-dependent transmission conditions. Filomat, Tome 36 (2022) no. 10, p. 3355 . doi: 10.2298/FIL2210355T
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     author = {M M Tharwat},
     title = {On {Dirac} systems with multi-eigenparameter-dependent transmission conditions},
     journal = {Filomat},
     pages = {3355 },
     year = {2022},
     volume = {36},
     number = {10},
     doi = {10.2298/FIL2210355T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2210355T/}
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