Eigenvalues of Sturm-Liouville problems with distribution potentials on time scales

References

• R. Agarwal, M. Bohner, and P. Wong, Sturm-Liouville eigenvalue problems on time scales, Appl. Math. Comput. 99 (1999), 153–166.
   Web of Science ®Google Scholar
• Z. Akdoğan, M. Demirci, and O. Mukhtarov, Green function of discontinuous boundary-value problem with transmission conditions, Math. Meth. Appl. Sci. 30 (2007), 1719–1738.
   Web of Science ®Google Scholar
• S. Albeverio, F. Gesztesy, R. Høegh-Krohn, and H. Holden, Solvable Models in Quantum Mechanics, Sec. Edition, AMS Chelsea Publ., Providence, RI, 2005.
   Google Scholar
• J. Ao and J. Sun, Matrix representations of Sturm-Liouville problems with eigenparameter-dependent boundary conditions, Linear Algebra Appl. 438 (2013), 2359–2365.
   Web of Science ®Google Scholar
• J. Ao and J. Sun, Matrix representations of Sturm-Liouville problems with coupled eigenparameter-dependent boundary conditions, Appl. Math. Comput. 244 (2014), 142–148.
   Web of Science ®Google Scholar
• J. Ao, J. Sun, and M. Zhang, The finite specturm of Sturm-Liouvolle problems with transmission conditions, Appl. Math. Comput. 218 (2011), 1166–1173.
   Web of Science ®Google Scholar
• F. Atkinson, Discrete and Continuous Boundary Problems, Academic Press, New York/London, 1964.
   Google Scholar
• P. Binding, P. Browne, and B. Watson, Sturm-Liouville problems with boundary conditions rationally dependent on the eigenparameter, J. Comp. Appl. Math. 148 (2002), 147–168.
   Web of Science ®Google Scholar
• P. Binding, P. Browne, and B. Watson, Inverse spectral problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions, Proc. London Math. Soc. 62 (2004), 161–182.
   Google Scholar
• M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkäuser, Boston, (2001).
   Google Scholar
• J. Eckhardt, F. Gesztesy, R. Nichols, and G. Teschl, Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional potentials, Opuscula Math. 33 (2013), 467–563.
   Google Scholar
• C. Fulton and S. Pruess, Numerical methods for a singular eigenvalue problem with eigenparameter in the boundary conditions, J. Math. Anal. Appl. 71 (1979), 431–462.
   Web of Science ®Google Scholar
• Q. Kong, Sturm-Liouville eigenvalue problems on time scales with separated boundary conditions, Results Math. 52 (2008), 111–121.
   Web of Science ®Google Scholar
• Q. Kong, H. Volkmer, and A. Zettl, Matrix representations of Sturm-Liouville problems with finite spectrum, Results. Math. 54 (2009), 103–116.
   Web of Science ®Google Scholar
• Q. Kong, H. Wu, and A. Zettl, Sturm-Liouville problems with finite spectrum, J. Math. Anal. Appl. 263 (2001), 748–762.
   Web of Science ®Google Scholar
• Q. Kong and A. Zettl, Inverse Sturm-Liouville problems with finite spectrum, J. Math. Anal. Appl. 386 (2012), 1–9.
   Web of Science ®Google Scholar
• P. Kurasov, On the Coulomb potential in one dimension, J. Phys. A. 29 (1996), 1767–1771.
   Google Scholar
• K. Mirzoev and N. Konechnaya, Singular Sturm-Liouville operators with distribution potentials, J. Math. Sci. 200 (2014), 96–105.
   Google Scholar
• M. Moshinsky, Penetrability of a one-dimensional Coulomb potential, J. Phys. A. 27, (1993), 2445–2450.
   Google Scholar
• H. Olğar and O. Mukhtarov, Weak eigenfunction of two-interval Sturm-Liouville problems together with interaction conditions, J. Math. Phys. 58(4) (2017), 388–396.
   Web of Science ®Google Scholar
• N. Pronska, Reconstruction of energy-dependent Sturm-Liouville equations from two spectra, Integr. Equ. Oper. Theory 76 (2013), 403–419.
   Web of Science ®Google Scholar
• A. Savchuk and A. Shkalikov, Inverse problem for Sturm-Liouville operators with distribution potentials: reconstruction from two spectra, Russ. J. Math. Phys. 12 (2005), 507–514.
   Web of Science ®Google Scholar
• H. Tuna, Completeness theorem for the dissipative Sturm-Liouville operator on bounded time scales, Indian J. Pure Appl. Math. 47 (2016), 535–544.
   Web of Science ®Google Scholar
• A. Zettl, Sturm-Liouville Theory, Mathematical Surveys and Monographs, Vol. 121, Amer. Math. Soc., Providence, RI, 2005.
   Google Scholar
• C. Zhang and D. Yang, Eigenvalues of second-order linear equations with coupled boundary conditions on time scales, Appl. Math. Comput. 33 (2010), 1–21.
   Google Scholar