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Abstrakty
In this paper, asymptotic formulae for solutions and Green’s function of a boundary value problem are investigated when the equation and the boundary conditions contain a spectral parameter.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
651--661
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
- Karadeniz Technical University, Department of Mathematics, Trabzon, Turkey
Bibliografia
- [1] K. Aydemir, Boundary value problems with eigenvalue-dependent boundary and transmission condition, Bound. Value Probl. 2014 (2014), Article no. 131.
- [2] E. Başkaya, Asymptotics of eigenvalues for Sturm–Liouville problem including eigenparameter-dependent boundary conditions with integrable potential, NTMSCI 6 (2018), 39–47.
- [3] E. Başkaya, Asymptotics of eigenvalues for Sturm–Liouville problem including quadratic eigenvalue in the boundary condition, NTMSCI 6 (2018), 76–82.
- [4] E. Başkaya, Asymptotics of eigenvalues for Sturm–Liouville problem with eigenparameter dependent-boundary conditions, NTMSCI 6 (2018), 247–257.
- [5] E. Başkaya, Periodic and semi-periodic eigenvalues of Hill’s equation with symmetric double well potential, TWMS J. App. Eng. Math. 10 (2020), 346–352.
- [6] E. Başkaya, Asymptotic eigenvalues of regular Sturm–Liouville problems with spectral parameter-dependent boundary conditions and symmetric single well potential, Turk. J. Math. Comput. Sci. 13 (2021), 44–50.
- [7] E. Başkaya, On the gaps of Neumann eigenvalues for Hill’s equation with symmetric double well potential, Tbillisi Math. J. 8 (2021), 139–145.
- [8] P.A. Binding, P.J. Browne, B.A. Watson, Sturm–Liouville problems with reducible boundary conditions, Proc. Edinburgh Math. Soc. 49 (2006), 593–608.
- [9] H. Coşkun, E. Başkaya, Asymptotics of eigenvalues of regular Sturm–Liouville problems with eigenvalue parameter in the boundary condition for integrable potential, Math. Scand. 107 (2010), 209–223.
- [10] H. Coşkun, E. Başkaya, Asymptotics of eigenvalues for Sturm–Liouville problem with eigenvalue in the boundary condition for differentiable potential, APAM 16 (2018), 7–19.
- [11] H. Coşkun, E. Başkaya, A. Kabataş, Instability intervals for Hill’s equation with symmetric single well potential, Ukr. Math. J. 71 (2019), 977–983.
- [12] H. Coşkun, A. Kabataş, Asymptotic approximations of eigenfunctions for regular Sturm–Liouville problems with eigenvalue parameter in the boundary condition for integrable potential, Math. Scand. 113 (2013), 143–160.
- [13] H. Coşkun, A. Kabataş, Green’s function of regular Sturm–Liouville problem having eigenparameter in one boundary condition, Turkish J. Math. and Comput. Sci. 4 (2016), 1–9.
- [14] H. Coşkun, A. Kabataş, E. Başkaya, On Green’s function for boundary value problem with eigenvalue dependent quadratic boundary condition, Bound. Value Probl. 2017 (2017), Article no. 71.
- [15] D.G. Duffy, Green’s Functions with Applications Chapman Hall/CRC, New York, 2015.
- [16] C.T. Fulton, Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 293–308.
- [17] B.J. Harris, The form of the spectral functions associated with Sturm–Liouville problems with continuous spectrum, Mathematika 44 (1997), 149–161.
- [18] H. Hochstadt, Estimates on the stability intervals for Hill’s equation, Proc. Am. Math. Soc. 14 (1963), 930–932.
- [19] Ch.G. Ibadzadeh, I.M. Nabiev, Reconstruction of the Sturm–Liouville operator with nonseparated boundary conditions and a spectral parameter in the boundary condition, Ukr. Math. J. 69 (2018), 1416–1423.
- [20] A. Kabataş, Eigenfunction and Green’s function asymptotics for Hill’s equation with symmetric single well potential, Ukr. Math. J. 74 (2022), 218–231.
- [21] A. Kabataş, On eigenfunctions of Hill’s equation with symmetric double well potential, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 71 (2022), 634–649.
- [22] N.B. Kerimov, Kh.R. Mamedov, On one boundary value problem with a spectral parameter in the boundary conditions, Sib. Math. J. 40 (1999), 281–290.
- [23] H.Y. Zhang, J.J. Ao, M.L. Li, Dependence of eigenvalues of Sturm–Liouville problems with eigenparameter-dependent boundary conditions and interface conditions, Mediterr. J. Math. 19 (2022), Article no. 90.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
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