Reconstruction for Sturm–Liouville equations with a constant delay with twin-dense nodal subsets

References

• Hale J. Theory of functional-differential equations. New York (NY): Springer-Verlag; 1977.
   Google Scholar
• Buterin SA, Yurko VA. Sturm-Liouville differential operators with deviating argument. Tamkang J Math. 2017;46(1):61–71.
   Google Scholar
• Freiling G, Yurko VA. Inverse problems for Sturm-Liouville differential operators with a constant delay. Appl Math Lett. 2012;25:1999–2004. doi: 10.1016/j.aml.2012.03.026
   Web of Science ®Google Scholar
• Pikula M. Determination of a Sturm-Liouville-type differential operator with delay argument from two spectra. Mat Vesnik. 1991;43(3–4):159–171.
   Google Scholar
• Vladičić V, Pikula M. An inverse problem for Sturm-Liouville-type differential equation with a constant delay. Sarajevo J Math. 2016;12(1):83–88. doi: 10.5644/SJM.12.1.06
   Google Scholar
• Vlasov VV. On the solvability and properties of solutions of functional-differential equations in a Hilbert space. Mat Sb. 1995;186(8):67–92. (in Russian); English transl in Sb Math. 186(8)(1995), 1147–1172
   Google Scholar
• Kuryshova YV, Shieh CT. An inverse nodal problem for integro-differential operators. J Inverse Ill-Posed Probl. 2010;18:357–369. doi: 10.1515/jiip.2010.014
   Web of Science ®Google Scholar
• Freiling G, Yurko VA. Inverse Sturm-Liouville problems and their applications. New York (NY): Nova Science Publishers; 2001.
   Google Scholar
• Gesztesy F, Simon B. Inverse spectral analysis with partial information on the potential II: the case of discrete spectrum. Trans Amer Math Soc. 2000;352:2765–2787. doi: 10.1090/S0002-9947-99-02544-1
   Web of Science ®Google Scholar
• Horvath M. On the inverse spectral theory of Schrödinger and Dirac operators. Trans Amer Math Soc. 2001;353:4155–4171. doi: 10.1090/S0002-9947-01-02765-9
   Web of Science ®Google Scholar
• Rundell W, Sacks PE. The reconstruction of Sturm-Liouville operators. Inverse Probl. 1992;8:457–482. doi: 10.1088/0266-5611/8/3/007
   Web of Science ®Google Scholar
• Wang YP. Inverse problems for discontinuous Sturm-Liouville operators with mixed spectral data. Inverse Probl Sci Eng. 2015;23:1180–1198. doi: 10.1080/17415977.2014.981748
   Web of Science ®Google Scholar
• McLaughlin JR. Inverse spectral theory using nodal points as data-a uniqueness result. J Differential Equ. 1988;73:354–362. doi: 10.1016/0022-0396(88)90111-8
   Web of Science ®Google Scholar
• Browne PJ, Sleeman BD. Inverse nodal problem for Sturm-Liouville equation with eigenparameter dependent boundary conditions. Inverse Probl. 1996;12:377–381. doi: 10.1088/0266-5611/12/4/002
   Web of Science ®Google Scholar
• Cheng YH, Law CK, Tsay J. Remarks on a new inverse nodal problem. J Math Anal Appl. 2000;248:145–155. doi: 10.1006/jmaa.2000.6878
   Web of Science ®Google Scholar
• Currie S, Watson BA. Inverse nodal problems for Sturm-Liouville equations on graphs. Inverse Probl. 2007;23:2029–2040. doi: 10.1088/0266-5611/23/5/013
   Web of Science ®Google Scholar
• Guo Y, Wei G. Inverse problems: Dense nodal subset on an interior subinterval. J Differential Equ. 2013;255:2002–2017. doi: 10.1016/j.jde.2013.06.006
   Web of Science ®Google Scholar
• Koyunbakan H, Panakhov ES. A uniqueness theorem for inverse nodal problem. Inverse Probl Sci Eng. 2007;15(6):517–524. doi: 10.1080/00423110500523143
   Web of Science ®Google Scholar
• Law CK, Yang CF. Reconstructing the potential function and its derivatives using nodal data. Inverse Probl. 1998;14:299–312. doi: 10.1088/0266-5611/14/2/006
   Web of Science ®Google Scholar
• Shen CL. On the nodal sets of the eigenfunctions of the string equations. SIAM J Math Anal. 1988;19:1419–1424. doi: 10.1137/0519104
   Web of Science ®Google Scholar
• Shen CL, Shieh CT. An inverse nodal problem for vectorial Sturm-Liouville equation. Inverse Probl. 2000;16:349–356. doi: 10.1088/0266-5611/16/2/306
   Web of Science ®Google Scholar
• Shieh CT, Yurko VA. Inverse nodal and inverse spectral problems for discontinuous boundary value problems. J Math Anal Appl. 2008;347:266–272. doi: 10.1016/j.jmaa.2008.05.097
   Web of Science ®Google Scholar
• Wang WC, Cheng YH. On the existence of sign-changingradial solutions to nonlinear p-Laplacian equations in Rn. Nonlinear Anal Series A. 2014;102:14–22. doi: 10.1016/j.na.2014.01.027
   Web of Science ®Google Scholar
• Wang YP, Lien Ko Ya, Shieh CT. Inverse problems for the boundary value problem with the interior nodal subsets. Appl Anal. 2017;96(7):1229–1239. doi: 10.1080/00036811.2016.1183770
   Web of Science ®Google Scholar
• Wang YP, Shieh CT, Miao HY. Inverse transmission eigenvalue problems with the twin-dense nodal subset. J Inverse Ill-Posed Probl. 2017;25(2):237–249. doi: 10.1515/jiip-2016-0021
   Web of Science ®Google Scholar
• Wang YP, Yurko VA. On the inverse nodal problems for discontinuous Sturm-Liouville operators. J Differential Equ. 2016;260:4086–4109. doi: 10.1016/j.jde.2015.11.004
   Web of Science ®Google Scholar
• Yang CF. Solution to open problems of Yang concerning inverse nodal problems. Isr J Math. 2014;204:283–298. doi: 10.1007/s11856-014-1093-0
   Web of Science ®Google Scholar
• Yang XF. A new inverse nodal problem. J Differential Equ. 2001;169:633–653. doi: 10.1006/jdeq.2000.3911
   Web of Science ®Google Scholar
• Yurko VA. Inverse nodal problems for Sturm-Liouville operators on star-type graphs. J Inverse Ill-Posed Probl. 2008;16:715–722. doi: 10.1515/JIIP.2008.044
   Web of Science ®Google Scholar