Eigenparameter dependent Sturm–Liouville problems in boundary conditions with transmission conditions

Solvability and coerciveness of multi-point Sturm–Liouville problems with abstract linear functionals

“…Note that an abstract theory of the boundary value problems with continuous coefficients and an eigenvalue parameter in the boundary conditions have been constructed by Yakubov and Yakubov (see [4] and corresponding bibliography). Many authors have been devoted to the study of discontinuous problems [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. To deal with the discontinuity of the problem, transmission conditions are imposed on the discontinuous points.…”

A discontinuous Sturm–Liouville problem with boundary conditions rationally dependent on the eigenparameter

“…To deal with interior discontinuities, some conditions, which are often called transmission conditions [10][11][12][13], interface conditions [14,16], are imposed on the discontinuous points. Mukhtarov et al in [13] considered eigenparameter dependent Sturm-Liouville problems with transmission conditions and obtained some properties of eigenvalues.…”

“…Also, a two interior discontinuous points case was investigated in [18,20]. Numerous authors have been devoted to this area (see [10][11][12][13][14][15][16][17][18][19][20]). By using Mukhtarov's method (see, for example, [10,12,13,20]), the authors defined a new inner product in the direct sum of classical Hilbert spaces in such a way that the considered problem can be interpreted as an eigenvalue problem for a self-adjoint operator with compact resolvent.…”

On the completeness of eigenfunctions of a discontinuous Dirac operator with an eigenparameter in the boundary condition

“…Discontinuous boundary-value problems arise in different areas of mathematics, radio science, electronics, geophysics and mechanics [5]. Boundary value problems with transmission conditions were investigated in [1,3,4,7] and [14]- [19].…”