Yuping Wang1, Yan-Hsiou Cheng2, Xianbiao Wei3,*
1Department of Applied Mathematics, Nanjing Forestry University, Nanjing, Jiangsu, China.
2Department of Mathematics and Information Education, National Taipei University of Education, Taipei, Taiwan.
3Department of Mathematics and Physics, Anhui Jianzhu University, Hefei, Anhui, China.
*Corresponding author:Xianbiao Wei
References
[1] Bondarenko, N.P. (2018). A partial inverse problem for the Sturm-Liouville operator on a star-shaped graph. Anal. Math. Phy., 8, 155-168.
[2] Cheng,Y.H., Law, C.K.J. (2000). Remarks on a new inverse nodal problem. J. Math. Anal. Appl., 248, 145-155.
[3] Cheng,Y.H. (2012). Reconstruction of the Sturm-Liouville operator on a p-star graph with nodal data. Rocky Mt. J. Math., 42(5), 1431-1446.
[4] Currie, S., Watson, B.A. (2007). Inverse nodal problems for Sturm-Liouville equations on graphs. Inverse Problems, 23, 2029-2040.
[5] Gesztesy, F., Simon, B. (2000). Inverse spectral analysis with partial information on the potential II: The case of discrete spectrum, Trans. Amer. Math. Soc., 352, 2765-2787.
[6] Guo,Y., Wei, G. (2019). The sharp conditions of the uniqueness for inverse nodal problems. J. Diff. Equ., 266, 4432-4449.
[7] Kuchment, P., Post, O. (2007). On the spectra of carbon nano-structures. Comm. Math. Phys., 275, 805-826.
[8] Hald, O.H., McLaughlin, J.R. (1989). Solutions of inverse nodal problems. Inverse Problems, 5, 307-347.
[9] Horváth, M. (2001). On the inverse spectral theory of Schrödinger and Dirac operators. Trans.Amer. Math. Soc., 353, 4155-4171.
[10] Levinson, N. (1940). Gap and density theorems, AMS Coll. Publ., New York.
[11] Levin, B.Ja. (1956). Distribution of zeros of entire functions (in Russian). GITTL, Moscow,.
[12] McLaughlin, J.R. (1988). Inverse spectral theory using nodal points as data-a uniqueness result. J. Diff. Equ., 73, 354-362.
[13] Wang,Y.P., Shieh,C.-T. (2021). Inverse problems for Sturm-Liouville operators on a compact equilateral graph by partial nodal data. Math. Meth. Appl. Sci., 44, 693-704.
[14] Wang, Y.P., Shieh, C.-T., Wei, X. (2020). Partial inverse nodal problems for differential pencils on a star-shaped graph. Math. Meth. Appl. Sci., 43(15), 8841-8855.
[15] Wei, X., Cheng, Y.H., Wang, Y.P. (2022). The Partial Inverse Spectral and Nodal Problems for Sturm-Liouville Operators on a Star-Shaped Graph. Mathematics, 10, 3971. https://doi.org/10.3390/math10213971.
[16] Yang, C.-F., Guan, S.-Y. (2021). Reconstruction of the Sturm-Liouville operator on a graph from subinterval nodes. Taiwanese J. Math., 25(5), 1041-1052.
[17] Yang, X.F. (2001). A new inverse nodal problem. J. Diff. Equ., 169(2), 633-653.
[18] Yurko, V.A. (2008). Inverse nodal problems for Sturm-Liouville operators on star-type graphs. J. Inverse Ill-Posed Problems, 16, 715-722.
[19] Freiling, G., Yurko, V.A. (2001). Inverse Sturm-Liouville Problems and their Applications. New York: Nova Science Publishers.