Inverse Nodal Problems for Dirac-Type Integro-Differential System with Boundary Conditions Polynomially Dependent on the Spectral Parameter
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
Supporting Institution
Project Number
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.