Inverse nodal problem for a Sturm-Liouville operator with discontinuous coefficient

Year 2017, Volume: 66 Issue: 1, 165 - 171, 01.02.2017

Sinan Özkan A.

https://doi.org/10.1501/Commua1_0000000785

Cited By: 1

https://izlik.org/JA52KU92ET

Abstract

Inverse nodal problem for SturmñLiouville equation with discontinuity coeffecient is studied. A uniqueness theorem and an algorithm for
recovering the coeffecient of the problem from a known sequence related to
the nodal points are given

Keywords

Sturm-Liouville equation , inverse nodal problem , discontinuitycondition

References

• R.Kh. Amirov, A.S. Ozkan, Discontinuous Sturm-Liouville Problems with Eigenvalue De- pendent Boundary Condition, Math Phys Anal Geom, 17, 483-491, doi:10.1007/s11040-014- 1
• L. Andersson, Inverse eigenvalue problems with discontiuous coe¢ cients, Inverse Problems, , (1988), 353-397.
• M.I. Belishev, Inverse spectral inde…nite problem for the equation y00+ p(x)y = 0on an interval, Funkts. Anal. Prilozh., 21(2) (1987), 68-69.
• P.J. Browne, B.D. Sleeman, Inverse nodal problem for Sturm–Liouville equation with eigen- parameter depend boundary conditions, Inverse Problems 12 (1996), pp. 377–381.
• S.A. Buterin, C.T. Shieh, Inverse nodal problem for diğerential pencils, Appl. Math. Lett. , (2009), 1240–1247.
• S.A. Buterin, C.T. Shieh, Incomplete inverse spectral and nodal problems for diğerential pencil. Results Math. 62, (2012), 167-179
• R. Carlson, An inverse spectral problem for Sturm-Liouville operators with discontiuous coe¢ cients, Proceed. Amer. Math. Soc., 120(2), (1994), 475-484.
• Y.H. Cheng, C-K. Law and J. Tsay, Remarks on a new inverse nodal problem, J. Math. Anal. Appl. 248, (2000), pp. 145–155.
• C.F. Coleman, J.R. McLaughlin, Solution of inverse spectral problems for an impedance with integrable derivative, I, II, Comm. Pure and Appl. Math., 46, (1993), 145-184, 185-212.
• S. Currie, B.A. Watson, Inverse nodal problems for Sturm–Liouville equations on graphs, Inv. Probl. 23, (2007), pp. 2029–2040.
• G. Freiling, V.A. Yurko, Inverse problems for diğerential equations with turning points, In- verse Problems 13, (1997), 1247-1263.
• Y.X. Guo, G.S. Wei Inverse problems: Dense nodal subset on an interior subinterval, J. Diğerential Equations, 255(7), (2013), 2002–2017.
• O.H. Hald, J.R. McLaughlin, Solutions of inverse nodal problems, Inv. Prob. 5 (1989), pp. –347.
• C.K. Law, J. Tsay, On the well-posedness of the inverse nodal problem, Inv. Probl. 17 (2001), pp. 1493–1512.
• J.R. McLaughlin, Analytical methods for recovering coe¢ cients in diğerential equations from spectral data, SIAM Rev., 28, (1986), 53-72.
• A. McNabb, R. Anderssen and E. Lapwood, Asymptotic behaviour of the eigenvalues of a Sturm–Liouville system with discontiuous coe¢ cients, J. Math. Anal. Appl., 54, (1976), 751.
• J.R. McLaughlin, Inverse spectral theory using nodal points as data – a uniqueness result, J. Diğ. Eq. 73 (1988), pp. 354–362. A.S. Ozkan,B. Keskin
• Inverse nodal problems for Sturm–Liouville equation with eigenparameter-dependent boundary and jump conditions, Inverse Problems in Science and Engineering, i-…rst, (2014), doi:10.1080/17415977.2014.991730.
• C.L. Shen, C.T. Shieh, An inverse nodal problem for vectorial Sturm–Liouville equation, Inv. Probl. 16 (2000), pp. 349–356.
• C-T Shieh, V. A. Yurko, Inverse nodal and inverse spectral problems for discontinuous bound- ary value problems, J. Math. Anal. Appl. 347 (2008) 266-272.
• X-F Yang, A solution of the nodal problem, Inverse Problems, 13, (1997) 203-213.
• X-F. Yang, A new inverse nodal problem, J. Diğer. Eqns. 169 (2001), pp. 633–653.
• 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, (7), (2011), 951-961.
• C-F. Yang, Inverse nodal problems of discontinuous Sturm–Liouville operator, J. Diğerential Equations, 254, (2013) 1992–2014.