[1]

Aktosun T., Gintides D. and Papanicolaou V. G.,
The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation,
Inverse Problems 27 (2011), Article ID 115004.
Google Scholar

[2]

Buterin S. A. and Shieh C. T.,
Inverse nodal problem for differential pencils,
Appl. Math. Lett. 22 (2009), 1240–1247.
Google Scholar

[3]

Buterin S. A., Yang C. F. and Yurko V. A.,
On an open question in the inverse transmission eigenvalue problem,
Inverse Problems 31 (2015), Article ID 045003.
Google Scholar

[4]

Cakoni F., Colton D. and Haddar H.,
On the determination of Dirichlet or transmission eigenvalues from far field data,
C. R. Math. Acad. Sei. Paris. Ser. I 348 (2010), 379–383.
Google Scholar

[5]

Cakoni F., Gintides D. and Haddar H.,
The existence of an infinite discrete set of transmission eigenvalues,
SIAM J. Math. Anal. 42 (2010), 237–255.
Google Scholar

[6]

Cakoni F. and Haddar H.,
Transmission eigenvalue in scattering theory,
Inverse Problems and Applications. Inside Out II,
Math. Sci. Res. Inst. Publ. 60,
Cambridge University Press, New York (2012), 527–578.
Google Scholar

[7]

Cheng Y. H., Law C. K. and Tsay J.,
Remarks on a new inverse nodal problem,
J. Math. Anal. Appl. 248 (2000), 145–155.
Google Scholar

[8]

Colton D., Kirsch A. and Päivärinta A.,
Far-field patterns for acoustic waves in an inhomogeneous medium,
SIAM J. Math. Anal. 20 (1989), 1472–1483.
Google Scholar

[9]

Colton D. and Leung Y.-J.,
Complex eigenvalues and the inverse spectral problem for transmission eigenvalues,
Inverse Problems 29 (2013), Article ID 104008.
Google Scholar

[10]

Freiling G. and Yurko V. A.,
Inverse Sturm–Liouville Problems and Their Applications,
NOVA Science, New York, 2001.
Google Scholar

[11]

Gesztesy F. and Simon B.,
Inverse spectral analysis with partial information on the potential II: The case of discrete spectrum,
Trans. Amer. Math. Soc. 352 (2000), 2765–2787.
Google Scholar

[12]

Guo Y. and Wei G.,
Inverse problems: Dense nodal subset on an interior subinterval,
J. Differential Equations 255 (2013), 2002–2017.
Google Scholar

[13]

Kirsch A.,
On the existence of transmission eigenvalues,
Inverse Probl. Imaging 3 (2009), 155–172.
Google Scholar

[14]

Ledoux V., Van Daele M. and Vanden Berghe G.,
MATSLISE: A MATLAB package for the numerical solution of Sturm–Liouville and Schrödinger equations,
ACM Trans. Math. Software 31 (2005), 532–554.
Google Scholar

[15]

Marchenko V. A.,
Some questions in the theory of one-dimensional linear differential operators of the second order I (in Russian),
Trudy Moskov. Mat. Obsc. 1 (1952), 327–420;
translation in Amer. Math. Soc. Transl. 101 (1973), no. 2, 1–104.
Google Scholar

[16]

McLaughlin J. R.,
Inverse spectral theory using nodal points as data-a uniqueness result,
J. Differential Equations 73 (1988), 354–362.
Google Scholar

[17]

Mclaughlin J. R. and Polyakov P. L.,
On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues,
J. Differential Equations 107 (1994), 351–382.
Google Scholar

[18]

Rundell W. and Sacks P. E.,
The reconstruction of Sturm–Liouville operators,
Inverse Problems 8 (1992), 457–482.
Google Scholar

[19]

Rynne B. P. and Sleeman B. D.,
The interior transmission problem and inverse scattering from inhomogeneous media,
SIAM J. Math. Anal. 22 (1991), 1755–1762.
Google Scholar

[20]

Shen C. L.,
On the nodal sets of the eigenfunctions of the string equations,
SIAM J. Math. Anal. 19 (1988), 1419–1424.
Google Scholar

[21]

Shen C. L. and Shieh C. T.,
An inverse nodal problem for vectorial Sturm–Liouville equation,
Inverse Problems 16 (2000), 349–356.
Google Scholar

[22]

Wang W. C. and Cheng Y. H.,
On the existence of sign-changingradial solutions to nonlinear *p*-Laplacian equations in ${\mathbb{R}}^{n}$,
Nonlinear Anal. 102 (2014), 14–22.
Google Scholar

[23]

Wang Y. P., Huang Z. Y. and Yang C. F.,
Reconstruction for the spherically symmetric speed of sound from nodal data,
Inverse Probl. Sci. Eng. 21 (2013), 1032–1046.
Google Scholar

[24]

Wang Y. P. and Yurko V. A.,
On the inverse nodal problems for discontinuous Sturm–Liouville operators,
J. Differential Equations 260 (2016), 4086–4109.
Google Scholar

[25]

Yang C. F.,
Stability in the inverse nodal solution for the interior transmission problem,
J. Differential Equations 260 (2016), 2490–2506.
Google Scholar

[26]

Yang X. F.,
A solution of the inverse nodal problem,
Inverse Problems 13 (1997), 203–213.
Google Scholar

[27]

Yang C. F. and Buterin S.,
Uniqueness of the interior transmission problem with partial information on the potential and eigenvalues,
J. Differential Equations 260 (2016), 4871–4887.
Google Scholar

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