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Abstract:

In this paper we study an inverse problem for weighted second order Sturm-Liouville equations. We show that the zeros of any subsequence of eigenfunctions, or a dense set of nodes, are enough to determine the weight. We impose weaker hypotheses for positive weights, and we generalize the proof to include indefinite weights. Moreover, the parameters in the boundary conditions can be determined numerically by using a shooting method. © 2015 Elsevier Inc. All rights reserved.

Registro:

Documento: Artículo
Título:A nodal inverse problem for second order Sturm-Liouville operators with indefinite weights
Autor:Pinasco, J.P.; Scarola, C.
Filiación:Depto. de Matemática, IMAS-CONICET, Universidad de Buenos Aires, Pab. I Int. Guiraldes 2160, Buenos Aires, (1428), Argentina
Facultad de Ciencias Exactas y Naturales, Universidad Nacional de la Pampa, Uruguay 151, Santa Rosa, La Pampa, (6300), Argentina
Palabras clave:Eigenvalues; Indefinite weights; Inverse problems; Nodal points; Differential equations; Eigenvalues and eigenfunctions; Liouville equation; Eigenvalues; Indefinite weights; Nodal points; Second orders; Shooting methods; Sturm-Liouville equation; Sturm-Liouville operators; Inverse problems
Año:2015
Volumen:256
Página de inicio:819
Página de fin:830
DOI: http://dx.doi.org/10.1016/j.amc.2015.01.101
Título revista:Applied Mathematics and Computation
Título revista abreviado:Appl. Math. Comput.
ISSN:00963003
CODEN:AMHCB
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00963003_v256_n_p819_Pinasco

Referencias:

  • Billingsley, P., (1968) Convergence of Probability Measures, , Wiley New York
  • Borg, G., Eine umkehrung der Sturm-Liouvilleschen eigenwertaufgabe (1946) Acta Math., 78, pp. 1-96
  • Cantrell, R.S., Cosner, C., Diffusive logistic equations with indefinite weights: Population models in disrupted environments. II (1991) SIAM J. Math. Anal., 22, pp. 1043-1064
  • Cheng, Y.H., Law, C.K., The inverse nodal problem for Hill's equation (2006) Inverse Prob., 22, pp. 891-901
  • Chladni, E., (1787) Entdeckungen Uber Die Theorie des Klanges
  • Dym, H., McKean, H.P., (1976) Gaussian Processes, Function Theory, and the Inverse Spectral Problem, , Academic Press New York
  • Eckhardt, J., Kostenko, A., (2014) The Inverse Spectral Problem for Indefinite Strings, , preprints
  • Fernández Bonder, J., Pinasco, J.P., Asymptotic behavior of the eigenvalues of the one-dimensional weighted p-Laplace operator (2003) Arkiv Math., 41, pp. 267-280
  • Hald, O.H., McLaughlin, J.R., Solution of inverse nodal problems (1989) Inverse Prob., 5, pp. 307-347
  • Hald, O.H., McLaughlin, J.R., Inverse problems: Recovery of BV coefficients from nodes (1998) Inverse Prob., 14, pp. 245-273
  • Gelfand, I.M., Levitan B, M., On the determination of a differential equation from its spectral function (1955) Trans. Am. Math. Soc., (2), pp. 253-304. , Translated from Izv. Akad. Nauk SSSR 15 (1951)
  • Gesztesy, F., Simon, B., Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum (2000) Trans. Am. Math. Soc., 352, pp. 2765-2787
  • Gladwell, G.M.L., (2004) Inverse Problems in Vibration, , vol. 119 Springer
  • Guo, Y., Wei, G., Inverse problems: Dense nodal subset on an interior subinterval (2013) J. Differ.Eqs., 255, pp. 2002-2017
  • Ince, E., (1956) Ordinary Differential Equations, , Dover New York
  • Lou, Y., Yanagida, E., Minimization of the principal eigenvalue for an elliptic boundary value problem with indefinite weight, and applications to population dynamics (2006) Jpn. J. Ind. Appl. Math., 23, pp. 275-292
  • Martínez-Finkelshtein, A., Martínez-González, P., Zarzo, A., WKB approach to zero distribution of solutions of linear second order differential equations (2002) J. Comput. Appl. Math., 145, pp. 167-182
  • Panakhov, E.S., Sat, M., Reconstruction of potential function for Sturm-Liouville operator with Coulomb potential (2013) Boundary Value Prob., 2013, pp. 1-9
  • Prokhorov, Yu.V., Convergence of random processes and limit theorems in probability theory (1956) Theor. Prob. Appl., 1, pp. 157-214
  • Shen, C.-L., On the nodal sets of the eigenfunctions of the string equation (1988) SIAM J. Math. Anal., 19, pp. 1419-1424
  • Shen, C.-L., Tsai, T.-M., On a uniform approximation of the density function of a string equation using eigenvalues and nodal points and some related inverse nodal problems (1995) Inverse Prob., 11, pp. 1113-1123
  • Wang, Y.-P., A uniqueness theorem for indefinite Sturm-Liouville Operators (2012) Appl. Math. J. Chin.Univ., 27, pp. 345-352

Citas:

---------- APA ----------
Pinasco, J.P. & Scarola, C. (2015) . A nodal inverse problem for second order Sturm-Liouville operators with indefinite weights. Applied Mathematics and Computation, 256, 819-830.
http://dx.doi.org/10.1016/j.amc.2015.01.101
---------- CHICAGO ----------
Pinasco, J.P., Scarola, C. "A nodal inverse problem for second order Sturm-Liouville operators with indefinite weights" . Applied Mathematics and Computation 256 (2015) : 819-830.
http://dx.doi.org/10.1016/j.amc.2015.01.101
---------- MLA ----------
Pinasco, J.P., Scarola, C. "A nodal inverse problem for second order Sturm-Liouville operators with indefinite weights" . Applied Mathematics and Computation, vol. 256, 2015, pp. 819-830.
http://dx.doi.org/10.1016/j.amc.2015.01.101
---------- VANCOUVER ----------
Pinasco, J.P., Scarola, C. A nodal inverse problem for second order Sturm-Liouville operators with indefinite weights. Appl. Math. Comput. 2015;256:819-830.
http://dx.doi.org/10.1016/j.amc.2015.01.101