BibTex RIS Kaynak Göster

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

Yıl 2017, Cilt: 66 Sayı: 1, 165 - 171, 01.02.2017
https://doi.org/10.1501/Commua1_0000000785

Öz

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

Kaynakça

  • 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.
Yıl 2017, Cilt: 66 Sayı: 1, 165 - 171, 01.02.2017
https://doi.org/10.1501/Commua1_0000000785

Öz

Kaynakça

  • 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.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Sinan Özkan A. Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 66 Sayı: 1

Kaynak Göster

APA Özkan A., S. (2017). Inverse nodal problem for a Sturm-Liouville operator with discontinuous coefficient. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(1), 165-171. https://doi.org/10.1501/Commua1_0000000785
AMA Özkan A. S. Inverse nodal problem for a Sturm-Liouville operator with discontinuous coefficient. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2017;66(1):165-171. doi:10.1501/Commua1_0000000785
Chicago Özkan A., Sinan. “Inverse Nodal Problem for a Sturm-Liouville Operator With Discontinuous Coefficient”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, sy. 1 (Şubat 2017): 165-71. https://doi.org/10.1501/Commua1_0000000785.
EndNote Özkan A. S (01 Şubat 2017) Inverse nodal problem for a Sturm-Liouville operator with discontinuous coefficient. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 1 165–171.
IEEE S. Özkan A., “Inverse nodal problem for a Sturm-Liouville operator with discontinuous coefficient”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 66, sy. 1, ss. 165–171, 2017, doi: 10.1501/Commua1_0000000785.
ISNAD Özkan A., Sinan. “Inverse Nodal Problem for a Sturm-Liouville Operator With Discontinuous Coefficient”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/1 (Şubat 2017), 165-171. https://doi.org/10.1501/Commua1_0000000785.
JAMA Özkan A. S. Inverse nodal problem for a Sturm-Liouville operator with discontinuous coefficient. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:165–171.
MLA Özkan A., Sinan. “Inverse Nodal Problem for a Sturm-Liouville Operator With Discontinuous Coefficient”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 66, sy. 1, 2017, ss. 165-71, doi:10.1501/Commua1_0000000785.
Vancouver Özkan A. S. Inverse nodal problem for a Sturm-Liouville operator with discontinuous coefficient. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(1):165-71.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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