Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2025, Cilt: 8 Sayı: 1, 49 - 56, 27.03.2025

Hanlar Reşidoğlu , Döne Karahan , Ufuk Çelik

https://doi.org/10.33434/cams.1605646

Öz

Kaynakça

  • [1] R. S. Anderssen, The effect of discontinuities in density and shear velocity on the asymptotic overtone structure of torsional eigenfrequencies of the Earth, Geophys. J. R. Astr. Soc., 50 (1997), 303-309.
  • [2] E. R. Lapwood, T. Usami, Free Oscillations of the Earth, Cambridge Univ. Press, Cambridge, 1981.
  • [3] O. H. Hald, Discontinuous inverse eigenvalue problems, Comm. Pure and Appl. Math., 37 (1984), 539-577.
  • [4] D. Shepelsky, The inverse problem of reconstruction of the medium’s conductivity in a class of discontinuous and increasing functions, Spectral operator theory and related topics: Adv. In Sov. Math., Providence, Amer. Math. Soc., 19 (1994), 209-232.
  • [5] M. Kobayashi, A uniqueness for discontinuous inverse Sturm-Liouville problems with symmetric potentials, Inverse Probl., 5 (1985), 767-781.
  • [6] G. Freiling, V. Yurko, On inverse Sturm-Liouville Problems and Their Applications, Nova Science Publisher Inc., New York, 2008.
  • [7] G. Freiling, V. Yurko, Lectures on Differential Equations of Mathematical Physics-A First Course, Nova Science Publisher Inc., New York, 2008.
  • [8] E. N. Akhmedova, On representation of solution of Sturm-Liouville equation with discontinuous coefficients, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerbaijan, 4 (2003), 7-18.
  • [9] E. N. Akhmedova, H. M. Huseynova, On eigenvalues and eigenfunctions of one class of Sturm-Liouville with discontinuous coefficients, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 23 (2003), 7-18.
  • [10] E. N. Akhmedova, The definition of one class of Sturm-Liouville Operators with discontinuous coefficients by Weyl function, Proceedings of IMM of NAS of Azerbaijan, 30 (2005), 3-8.
  • [11] D. Karahan, Kh. R. Mamedov, ˙I. F. Hashimoglu, On main equation for inverse Sturm–Liouville operator with discontinuous coefficient, Itogi Nauki Tekh. Ser. Sovrem. Mat. Prilozh. Temat. Obz., 225 (2023), 73-86.
  • [12] Kh. R. Mamedov, D. Karahan, On an inverse problem for Sturm-Liouville equation, EJPAM, 10 (2017), 535-543.
  • [13] Kh. R. Mamedov, F. A. Cetinkaya, Inverse problem for a class of Sturm-Liouville operator with spectral parameter in boundary condition, Bound. Value Probl., 2013 (2013), 183.
  • [14] Ö. Akçay, Kh. R. Mamedov, Inverse spectral problem for Dirac operators by spectral data, Filomat, 31 (2017), 1065-1077.
  • [15] R. Bellman, K. L. Kuk, Difference-Differential Equations, M. Mir., 1967.

On the Solution of a Class of Discontinuous Sturm-Liouville Problems

Yıl 2025, Cilt: 8 Sayı: 1, 49 - 56, 27.03.2025

Hanlar Reşidoğlu , Döne Karahan , Ufuk Çelik

https://doi.org/10.33434/cams.1605646

Öz

This study examines boundary value problems consisting of a second-order differential equation with discontinuous coefficients and boundary conditions. Asymptotic formulas for the eigenvalues and eigenfunctions of the problem are derived, and an expansion formula is obtained based on the eigenfunctions.

Anahtar Kelimeler

Asymptotic formulas Discontinuous coefficient Expansion formula Sturm-Liouville problem

Kaynakça

  • [1] R. S. Anderssen, The effect of discontinuities in density and shear velocity on the asymptotic overtone structure of torsional eigenfrequencies of the Earth, Geophys. J. R. Astr. Soc., 50 (1997), 303-309.
  • [2] E. R. Lapwood, T. Usami, Free Oscillations of the Earth, Cambridge Univ. Press, Cambridge, 1981.
  • [3] O. H. Hald, Discontinuous inverse eigenvalue problems, Comm. Pure and Appl. Math., 37 (1984), 539-577.
  • [4] D. Shepelsky, The inverse problem of reconstruction of the medium’s conductivity in a class of discontinuous and increasing functions, Spectral operator theory and related topics: Adv. In Sov. Math., Providence, Amer. Math. Soc., 19 (1994), 209-232.
  • [5] M. Kobayashi, A uniqueness for discontinuous inverse Sturm-Liouville problems with symmetric potentials, Inverse Probl., 5 (1985), 767-781.
  • [6] G. Freiling, V. Yurko, On inverse Sturm-Liouville Problems and Their Applications, Nova Science Publisher Inc., New York, 2008.
  • [7] G. Freiling, V. Yurko, Lectures on Differential Equations of Mathematical Physics-A First Course, Nova Science Publisher Inc., New York, 2008.
  • [8] E. N. Akhmedova, On representation of solution of Sturm-Liouville equation with discontinuous coefficients, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerbaijan, 4 (2003), 7-18.
  • [9] E. N. Akhmedova, H. M. Huseynova, On eigenvalues and eigenfunctions of one class of Sturm-Liouville with discontinuous coefficients, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 23 (2003), 7-18.
  • [10] E. N. Akhmedova, The definition of one class of Sturm-Liouville Operators with discontinuous coefficients by Weyl function, Proceedings of IMM of NAS of Azerbaijan, 30 (2005), 3-8.
  • [11] D. Karahan, Kh. R. Mamedov, ˙I. F. Hashimoglu, On main equation for inverse Sturm–Liouville operator with discontinuous coefficient, Itogi Nauki Tekh. Ser. Sovrem. Mat. Prilozh. Temat. Obz., 225 (2023), 73-86.
  • [12] Kh. R. Mamedov, D. Karahan, On an inverse problem for Sturm-Liouville equation, EJPAM, 10 (2017), 535-543.
  • [13] Kh. R. Mamedov, F. A. Cetinkaya, Inverse problem for a class of Sturm-Liouville operator with spectral parameter in boundary condition, Bound. Value Probl., 2013 (2013), 183.
  • [14] Ö. Akçay, Kh. R. Mamedov, Inverse spectral problem for Dirac operators by spectral data, Filomat, 31 (2017), 1065-1077.
  • [15] R. Bellman, K. L. Kuk, Difference-Differential Equations, M. Mir., 1967.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Adi Diferansiyel Denklemler, Fark Denklemleri ve Dinamik Sistemler
Bölüm Makaleler
Yazarlar

Hanlar Reşidoğlu 0000-0002-3283-9535

Döne Karahan 0000-0001-6644-5596

Ufuk Çelik 0009-0005-2982-725X

Erken Görünüm Tarihi 24 Mart 2025
Yayımlanma Tarihi 27 Mart 2025
Gönderilme Tarihi 22 Aralık 2024
Kabul Tarihi 14 Mart 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 8 Sayı: 1

Kaynak Göster

APA Reşidoğlu, H., Karahan, D., & Çelik, U. (2025). On the Solution of a Class of Discontinuous Sturm-Liouville Problems. Communications in Advanced Mathematical Sciences, 8(1), 49-56. https://doi.org/10.33434/cams.1605646
AMA Reşidoğlu H, Karahan D, Çelik U. On the Solution of a Class of Discontinuous Sturm-Liouville Problems. Communications in Advanced Mathematical Sciences. Mart 2025;8(1):49-56. doi:10.33434/cams.1605646
Chicago Reşidoğlu, Hanlar, Döne Karahan, ve Ufuk Çelik. “On the Solution of a Class of Discontinuous Sturm-Liouville Problems”. Communications in Advanced Mathematical Sciences 8, sy. 1 (Mart 2025): 49-56. https://doi.org/10.33434/cams.1605646.
EndNote Reşidoğlu H, Karahan D, Çelik U (01 Mart 2025) On the Solution of a Class of Discontinuous Sturm-Liouville Problems. Communications in Advanced Mathematical Sciences 8 1 49–56.
IEEE H. Reşidoğlu, D. Karahan, ve U. Çelik, “On the Solution of a Class of Discontinuous Sturm-Liouville Problems”, Communications in Advanced Mathematical Sciences, c. 8, sy. 1, ss. 49–56, 2025, doi: 10.33434/cams.1605646.
ISNAD Reşidoğlu, Hanlar vd. “On the Solution of a Class of Discontinuous Sturm-Liouville Problems”. Communications in Advanced Mathematical Sciences 8/1 (Mart 2025), 49-56. https://doi.org/10.33434/cams.1605646.
JAMA Reşidoğlu H, Karahan D, Çelik U. On the Solution of a Class of Discontinuous Sturm-Liouville Problems. Communications in Advanced Mathematical Sciences. 2025;8:49–56.
MLA Reşidoğlu, Hanlar vd. “On the Solution of a Class of Discontinuous Sturm-Liouville Problems”. Communications in Advanced Mathematical Sciences, c. 8, sy. 1, 2025, ss. 49-56, doi:10.33434/cams.1605646.
Vancouver Reşidoğlu H, Karahan D, Çelik U. On the Solution of a Class of Discontinuous Sturm-Liouville Problems. Communications in Advanced Mathematical Sciences. 2025;8(1):49-56.
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