The cubic eigenparameter dependent discrete Dirac equations with principal functions

Let us consider the Boundary Value Problem (BVP) for the discrete Dirac Equations

___

  • Agarwal, R. P. Difference equation and inequalities. 2000. Theory, Methods and Applications. Marcel Dekkar Inc., New York, Basel.
  • Agarwal, R. P. and Wong, P. J. Y. 1997. Advanced Topics in Difference Equations. Kluwer, Dordrecht.
  • Kelley, W. G. and Peterson, A. C. 2001. Difference Equations. An Introduction with Applications, Harcourt Academic Press.
  • Agarwal, R. P., Perera, K. and O'Regan, D. Multiple positive solutions of singular and nonsingular discrete problems via variational methods. Nonlinear Analysis, 2004, 58, 69-73.
  • Agarwal, R. P., Perera, K. and O'Regan, D. Multiple positive solutions of singular discrete p-Laplasian problems via variational methods. Advances in Difference Equations, 2005, 2005:2, 93-99.
  • Berezanski, Y. M. Integration of nonlinear difference equations by the inverse spectral problem method. Soviet Math. Dokl. 31, 1985, 264-267.
  • Toda, M. 1981. Theory of Nonlinear Lattices. Springer-Verlag, Berlin.
  • Bairamov, E. and Celebi, A. O. Spectrum and spectral expansion for the non-selfadjoint discrete Dirac operators. Quart. J. Math. Oxford, 1999, 50 (2), 371-384.
  • Bairamov, E., Cakar, O. and Krall, A. M. Non-selfadjoint difference operators and Jacobi matrices with spectral singularities. Math. Nachr., 2001, 229, 5-14.
  • Adivar, M. and Bairamov, E. Spectral properties of non-selfadjoint difference operators. J. Math. Anal. Appl., 2001, 261, 461-478.
  • Adivar, M. and Bairamov, E. Difference equations of second order with spectral singularities. J. Math. Anal. Appl., 2003, 277, 714-721.
  • Adivar, M. and Bohner, M. Spectral analysis of q-difference equations with spectral singularities. Math. Comput. Modelling, 2006, 43 (7-9), 695-703.
  • Adivar, M. and Bohner, M. Spectrum and principal vectors of second order q-difference equations. Indian J. Math., 2006, 48 (1),17-33.
  • Bairamov, E. and Coskun, C. Jost solutions and the spectrum of the system of difference equations. Appl. Math. Lett., 2004, 17, 1039-1045.
  • Bairamov, E. and Koprubasi, T. Eigenparameter dependent discrete Dirac equations with spectral singularities. Appl. Math. and Comp., 2010, 215, 4216-4220.
  • Aygar, Y., Olgun, M. and Koprubasi, T. Principal Functions of Nonselfadjoint Discrete Dirac Equations with Spectral Parameter in Boundary Conditions. Abstract and Applied Analysis, 2012, vol. 2012, ID 924628.
  • Koprubasi, T. Spectrum of the quadratic eigenparameter dependent discrete Dirac equations. Advances in Difference Equations, 2014, 2014:148.
  • Koprubasi, T. and Yokus, N. Quadratic eigenparameter dependent discrete Sturm Liouville equations with spectral singularities. Appl. Math. and Comp., 2014, 244, 57-62.
  • Levitan, B. M. and Sargsjan, I. S. Introduction to Spectral Theory. Translations of Mathematical Monographs, 1975, 39 .
  • Dolzhenko, E. P. Boundary value uniqueness theorems for analytic functions. Math. Notes, 1979, 26 (6), 437-442.