Local solvability and stability of the inverse problem for the non-self-adjoint Sturm–Liouville operator
Tóm tắt
We consider the non-self-adjoint Sturm–Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local solvability and stability of this inverse problem, relying on the method of spectral mappings. Possible splitting of multiple eigenvalues is taken into account.
Tài liệu tham khảo
Papageorgiou, N.S., Radulescu, V.D., Repovs, D.D.: Positive solutions for the perturbations of the Robin eigenvalue problem plus an indefinite potential. Discrete Contin. Dyn. Syst. 37(5), 2589–2618 (2017)
Bai, Y., Wang, W., Li, K.: Solvability and coerciveness of multi-point Sturm–Liouville problems with abstract linear functionals. Bound. Value Probl. 2019, Paper No. 17 (2019)
Bondarenko, N.: Spectral analysis of the matrix Sturm–Liouville operator. Bound. Value Probl. 2019, Paper No. 178 (2019)
Hwang, G.: The elliptic sinh-Gordon equation in a semi-strip. Adv. Nonlinear Anal. 8(1), 533–544 (2019)
Marchenko, V.A.: Sturm–Liouville Operators and Their Applications. Naukova Dumka, Kiev (1977) (Russian); English transl.: Birkhäuser (1986)
Levitan, B.M.: Inverse Sturm–Liouville Problems. Nauka, Moscow (1984) (Russian); English transl.: VNU Sci. Press, Utrecht (1987)
Pöschel, J., Trubowitz, E.: Inverse Spectral Theory. Academic Press, New York (1987)
Freiling, G., Yurko, V.: Inverse Sturm–Liouville Problems and Their Applications. Nova Science Publishers, Huntington (2001)
Gala, S., Liu, Q., Ragusa, M.A.: A new regularity criterion for the nematic liquid crystal flows. Appl. Anal. 91(9), 1741–1747 (2012)
Gala, S., Ragusa, M.A.: Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices. Appl. Anal. 95(6), 1271–1279 (2016)
Guo, Y., Wei, G., Yao, R.: An inverse three spectra problem for Sturm–Liouville operators. Bound. Value Probl. 2018, Paper No. 68 (2018)
Tkachenko, V.: Non-selfadjoint Sturm–Liouville operators with multiple spectra. In: Interpolation Theory, Systems Theory and Related Topics. Oper. Theory Adv. Appl., vol. 134, pp. 403–414. Birkhäuser, Basel (2002)
Buterin, S.A.: On inverse spectral problem for non-selfadjoint Sturm–Liouville operator on a finite interval. J. Math. Anal. Appl. 335(1), 739–749 (2007)
Yurko, V.A.: Method of Spectral Mappings in the Inverse Problem Theory. Inverse and Ill-Posed Problems Series. VNU Science, Utrecht (2002)
Buterin, S.A., Shieh, C.-T., Yurko, V.A.: Inverse spectral problems for non-selfadjoint second-order differential operators with Dirichlet boundary conditions. Bound. Value Probl. 2013, Paper No. 180 (2013)
Albeverio, S., Hryniv, R., Mykytyuk, Y.: On spectra of non-self-adjoint Sturm–Liouville operators. Sel. Math. New Ser. 13, 571–599 (2008)
Marletta, M., Weikard, R.: Weak stability for an inverse Sturm–Liouville problem with finite spectral data and complex potential. Inverse Probl. 21, 1275–1290 (2005)
Horvath, M., Kiss, M.: Stability of direct and inverse eigenvalue problems: the case of complex potentials. Inverse Probl. 27, 095007 (2011)
Bondarenko, N., Buterin, S.: On a local solvability and stability of the inverse transmission eigenvalue problem. Inverse Probl. 33, 115010 (2017)
Buterin, S., Kuznetsova, M.: On Borg’s method for non-selfadjoint Sturm–Liouville operators. Anal. Math. Phys. 9, 2133–2150 (2019)
Bondarenko, N.P.: Inverse Sturm–Liouville problem with analytical functions in the boundary condition. Open Math. 8(1), 512–528 (2020). https://doi.org/10.1515/math-2020-0188
Bondarenko, N.P.: Solvability and stability of the inverse Sturm–Liouville problem with analytical functions in the boundary condition. Math. Methods Appl. Sci. (2020). https://doi.org/10.1002/mma.6451