Research Article
BibTex RIS Cite

Inverse Nodal Problems for Dirac-Type Integro-Differential System with Boundary Conditions Polynomially Dependent on the Spectral Parameter

Year 2019, Volume: 40 Issue: 4, 875 - 885, 31.12.2019

Baki Keskin , Hediye Dilara Tel

https://doi.org/10.17776/csj.620668
Cited By: 2

Abstract

In this work, we study the inverse nodal problem
for Dirac type integro-differential operator with the boundary conditions
dependent spectral parameter polynomially. We prove that dense subset of the
nodal points determines the coefficients of differential part of operator and
gives partial information for integral part of it.

Keywords

Dirac operator Integro-differential operators Inverse nodal problem Parameter dependent boundary conditions.

Supporting Institution

CUBAP

Project Number

568

References

  • [1] J.R. McLaughlin, Inverse spectral theory using nodal points as data a uniqueness result, J. Diff. Eq. 73 (1988) 354-362.
  • [2] O.H. Hald, J.R. McLaughlin, Solutions of inverse nodal problems, Inv. Prob. 5 (1989) 307-347.
  • [3] X-F Yang, A solution of the nodal problem, Inverse Problems, 13 (1997) 203-213.
  • [4] P.J. Browne, B.D. Sleeman, Inverse nodal problem for Sturm-Liouville equation with eigenparameter depend boundary conditions, Inverse Problems 12 (1996) 377-381.
  • [5] S.A. Buterin, C.T. Shieh, Inverse nodal problem for differential pencils, Appl. Math. Lett. 22, (2009) 1240-1247.
  • [6] S.A. Buterin, C.T. Shieh, Incomplete inverse spectral and nodal problems for differential pencil. Results Math. 62 (2012) 167-179.
  • [7] Y.H. Cheng, C-K. Law and J. Tsay, Remarks on a new inverse nodal problem, J. Math. Anal. Appl. 248 (2000) 145-155.
  • [8] C.K. Law, C.L. Shen and C.F. Yang, The Inverse Nodal Problem on the Smoothness of the Potential Function, Inverse Problems, 15-1 (1999) 253-263 (Erratum, Inverse Problems, 17 (2001) 361-363.
  • [9] A.S. Ozkan, B. Keskin, Inverse Nodal Problems for Sturm-Liouville Equation with EigenparameterDependent Boundary and Jump Conditions, Inverse Problems in Science and Engineering, 23-8 (2015) 1306-1312.
  • [10] C-T Shieh, V.A. Yurko, Inverse nodal and inverse spectral problems for discontinuous boundary value problems, J. Math. Anal. Appl. 347 (2008) 266-272.
  • [11] C-F Yang, Xiao-Ping Yang, Inverse nodal problems for the Sturm-Liouville equation with polynomially dependent on the eigenparameter, Inverse Problems in Science and Engineering, 19-7 (2011) 951-961.
  • [12] C-F Yang, Inverse nodal problems of discontinuous Sturm-Liouville operator, J. Differential Equations, 254 (2013) 1992-2014.
  • [13] C-F Yang, Z-Y.Huang, Reconstruction of the Dirac operator from nodal data. Integr. Equ. Oper. Theory 66 (2010) 539-551.
  • [14] C-F Yang, V.N. Pivovarchik, : Inverse nodal problem for Dirac system with spectral parameter in boundary conditions. Complex Anal. Oper. Theory 7 (2013) 1211-1230.
  • [15] Y. Guo, Y. Wei, Inverse Nodal Problem for Dirac Equations with Boundary Conditions Polynomially Dependent on the Spectral Parameter, Results. Math. 67 (2015) 95--110.
  • [16] S.A. Buterin, On an Inverse Spectral Problem for a Convolution Integro-Differential Operator, Results in Mathematics, 50 (2007) 173-181.
  • [17] S.A. Buterin, The Inverse Problem of Recovering the Volterra Convolution Operator from the Incomplete Spectrum of its Rank-One Perturbation, Inverse Problems, 22 (2006) 2223--2236.
  • [18] G. Freiling, V.A. Yurko, Inverse Sturm--Liouville Problems and their Applications, Nova Science, New York, 2001.
  • [19] Y.V. Kuryshova, Inverse Spectral Problem for Integro-Differential Operators, Mathematical Notes, 81-6 (2007) 767-777.
  • [20] B.Wu, J. Yu, Uniqueness of an Inverse Problem for an Integro-Differential Equation Related to the Basset Problem, Boundary Value Problems, 229 (2014).
  • [21] B. Keskin A. S. Ozkan, Inverse nodal problems for Dirac-type integro-differential operators, J. Differential Equations. 263 (2017) 8838--8847
  • [22] B. Keskin, H. D. Tel, Reconstruction of the Dirac-Type Integro-Differential Operator From Nodal Data, Numerical Functional Analysis and Optimization, 39-11 (2018) 1208–1220.

Year 2019, Volume: 40 Issue: 4, 875 - 885, 31.12.2019

Baki Keskin , Hediye Dilara Tel

https://doi.org/10.17776/csj.620668
Cited By: 2

Abstract

Project Number

568

References

  • [1] J.R. McLaughlin, Inverse spectral theory using nodal points as data a uniqueness result, J. Diff. Eq. 73 (1988) 354-362.
  • [2] O.H. Hald, J.R. McLaughlin, Solutions of inverse nodal problems, Inv. Prob. 5 (1989) 307-347.
  • [3] X-F Yang, A solution of the nodal problem, Inverse Problems, 13 (1997) 203-213.
  • [4] P.J. Browne, B.D. Sleeman, Inverse nodal problem for Sturm-Liouville equation with eigenparameter depend boundary conditions, Inverse Problems 12 (1996) 377-381.
  • [5] S.A. Buterin, C.T. Shieh, Inverse nodal problem for differential pencils, Appl. Math. Lett. 22, (2009) 1240-1247.
  • [6] S.A. Buterin, C.T. Shieh, Incomplete inverse spectral and nodal problems for differential pencil. Results Math. 62 (2012) 167-179.
  • [7] Y.H. Cheng, C-K. Law and J. Tsay, Remarks on a new inverse nodal problem, J. Math. Anal. Appl. 248 (2000) 145-155.
  • [8] C.K. Law, C.L. Shen and C.F. Yang, The Inverse Nodal Problem on the Smoothness of the Potential Function, Inverse Problems, 15-1 (1999) 253-263 (Erratum, Inverse Problems, 17 (2001) 361-363.
  • [9] A.S. Ozkan, B. Keskin, Inverse Nodal Problems for Sturm-Liouville Equation with EigenparameterDependent Boundary and Jump Conditions, Inverse Problems in Science and Engineering, 23-8 (2015) 1306-1312.
  • [10] C-T Shieh, V.A. Yurko, Inverse nodal and inverse spectral problems for discontinuous boundary value problems, J. Math. Anal. Appl. 347 (2008) 266-272.
  • [11] C-F Yang, Xiao-Ping Yang, Inverse nodal problems for the Sturm-Liouville equation with polynomially dependent on the eigenparameter, Inverse Problems in Science and Engineering, 19-7 (2011) 951-961.
  • [12] C-F Yang, Inverse nodal problems of discontinuous Sturm-Liouville operator, J. Differential Equations, 254 (2013) 1992-2014.
  • [13] C-F Yang, Z-Y.Huang, Reconstruction of the Dirac operator from nodal data. Integr. Equ. Oper. Theory 66 (2010) 539-551.
  • [14] C-F Yang, V.N. Pivovarchik, : Inverse nodal problem for Dirac system with spectral parameter in boundary conditions. Complex Anal. Oper. Theory 7 (2013) 1211-1230.
  • [15] Y. Guo, Y. Wei, Inverse Nodal Problem for Dirac Equations with Boundary Conditions Polynomially Dependent on the Spectral Parameter, Results. Math. 67 (2015) 95--110.
  • [16] S.A. Buterin, On an Inverse Spectral Problem for a Convolution Integro-Differential Operator, Results in Mathematics, 50 (2007) 173-181.
  • [17] S.A. Buterin, The Inverse Problem of Recovering the Volterra Convolution Operator from the Incomplete Spectrum of its Rank-One Perturbation, Inverse Problems, 22 (2006) 2223--2236.
  • [18] G. Freiling, V.A. Yurko, Inverse Sturm--Liouville Problems and their Applications, Nova Science, New York, 2001.
  • [19] Y.V. Kuryshova, Inverse Spectral Problem for Integro-Differential Operators, Mathematical Notes, 81-6 (2007) 767-777.
  • [20] B.Wu, J. Yu, Uniqueness of an Inverse Problem for an Integro-Differential Equation Related to the Basset Problem, Boundary Value Problems, 229 (2014).
  • [21] B. Keskin A. S. Ozkan, Inverse nodal problems for Dirac-type integro-differential operators, J. Differential Equations. 263 (2017) 8838--8847
  • [22] B. Keskin, H. D. Tel, Reconstruction of the Dirac-Type Integro-Differential Operator From Nodal Data, Numerical Functional Analysis and Optimization, 39-11 (2018) 1208–1220.
There are 22 citations in total.

Details

Primary Language English
Journal Section Natural Sciences
Authors

Baki Keskin 0000-0003-1689-8954

Hediye Dilara Tel 0000-0003-1139-6146

Project Number 568
Publication Date December 31, 2019
Submission Date September 16, 2019
Acceptance Date December 30, 2019
Published in Issue Year 2019Volume: 40 Issue: 4

Cite

APA Keskin, B., & Tel, H. D. (2019). Inverse Nodal Problems for Dirac-Type Integro-Differential System with Boundary Conditions Polynomially Dependent on the Spectral Parameter. Cumhuriyet Science Journal, 40(4), 875-885. https://doi.org/10.17776/csj.620668

Cited By

Inverse Nodal Problems for Dirac-Type Integro-Differential Operators with Linear Functions in the Boundary Condition
Numerical Functional Analysis and Optimization
https://doi.org/10.1080/01630563.2022.2099419
Numerical solution and stability of the inverse spectral problem for a convolution integro-differential operator
Communications in Nonlinear Science and Numerical Simulation
Natalia Bondarenko
https://doi.org/10.1016/j.cnsns.2020.105298