Araştırma Makalesi
Yıl 2024,
Cilt: 13 Sayı: 3, 175 - 185, 31.12.2024
Öz
This study investigates a discontinuous Sturm-Liouville boundary value problem(BVP) on two intervals with functionals and transmission conditions in the direct sum ofSobolev spaces. Moreover, it presents the differential operator generated by the problem underinvestigation. The definition space of this operator is the direct sum of Sobolev spaces, andthe value space of the operator is the space obtained by adding the complex spaces where theboundary conditions are evaluated about the direct sum of Sobolev spaces. This paper establishesthe solvability of the problem and some important spectral properties of the operator, such asisomorphism, Fredholmness, and coerciveness concerning spectral parameters. In addition, theconclusion section discusses how different original problems can be produced.
Anahtar Kelimeler
BVP Functionaltransmission conditions Isomorphism Coerciveness Solvability
Etik Beyan
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Destekleyen Kurum
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Proje Numarası
-
Teşekkür
Thanks
Kaynakça
- I. Titeux, Y. Yakubov, Comletenes of root functions for the thermal condition in a strip with piecewise continuous coefficients, Mathematical Models and Methods in Applied Sciences 7 (7) (1997) 1035-1050.
- M. Kandemir, O. Sh. Mukhtarov, Many point boundary value problems for elliptic differentialoperator equations with interior singularities, Mediterranean Journal of Mathematics 17 (2020) Article Number 35 21 pages.
- O. Muhtarov, S. Yakubov, Problems for ordinary differential equations with transmission conditions, Applicable Analysis 81 (2002) 1033-1064.
- M. Kandemir, O. Sh. Mukhtarov, Nonlocal Sturm-Liouville problems with integral terms in the boundary conditions, Electronic Journal of Differential Equations 2017 (2017) Article Number 11 12 pages.
- M. Kandemir, Y.Yakubov, Regular boundary value problems with a discontinuous coefficient, functional-multipoint conditions and a linear spectral parameter, Israel Journal of Mathematics 180 (1) (2010) 255-270.
- O. Sh. Mukhtarov, Discontinuous boundary value problem with spectral parameter in boundary conditions, Turkish Journal of Mathematics 18 2 (1994) 183-192.
- O. Sh. Mukhtarov, K. Aydemir, Eigenfunction expansion for Sturm-Liouville problems with transmission conditions at one interior point, Acta Mathematica Scientia 35 (3) (2015) 639-649.
- A. V. Likov, Y. A. Mikhailov, The theory of heat and mass transfer, Qosenergaizdat (Russian), 1963.
- M. Kandemir, O. Sh. Mukhtarov, Y. Yakubov, Irregular boundary value problems with discontinuous coefficients and the eigenvalue parameter, Mediterranean Journal of Mathematics 6 (2009) 317-338.
- M. S. Alves, J. E. M. Rivera, M. Sepulveda, O. V. Villagran,Transmission problem in thermoelasticity, Hindawi 2011 (2011) Article Number 190548 33 pages.
- M. S. Agranovich, Spectral properties of diffraction problems, in: N. N. Voitovich, B. Z. Kazenelenbaum, A. N. Sivov (Eds.), The Generalized Method of Eigenoscillations in the Theory of Diffraction, Nauka, Moscow, 1977 (in Russian: translated into English Wiley-VCH, Berlin 1999).
- A. Stikonas, The Sturm-Liouville problem with a nonlocal boundary condition Lithuanian Mathematical Journal, 47 (3) (2007) 336-351.
- H. Triebel, Interpolation theory function spaces differential operators, in: M. Artin, H. Bass, J. Eells, W. Feit, P. J. Freyd, F. W. Gehring, H. Halberstam, L. V, Hormander, M. Kac, J. H. B. Kemperxuan, H. A. Lauwerier, W. A. J. Luxemburg, F, P. Peterson, I. M. Singer, and A. C. Zaanen (Eds.), Vol. 18, Nort Holland, Amsterdam, 1978.
- S. Yakubov, Y. Yakubov, Differential-operator equation ordinary and partial differential equation, in: A. Jeffrey, H. Brezis, R. G. Douglas (Eds.), Monographs and Surveys in Pure and Applied Mathematics, 1st Edition, Chapman and Hall/CRC, Boca Raton London, 1999.
- N. S. Imanbaev, M. A. Sadybekov, Characteristic determinant of the spectral problem for the ordinary differential operator with the boundary load, in: A. Ashyralyev, E. Malkowsky (Eds.), International Conference on Analysis and Applied Mathematics, Shymkent, 2014 - AIP Conference Proceedings 1611 (1) (2014) 261-265.
- V. B. Shakhmurov, Linear and nonlinear abstract elliptic equations with VMO coefficients and applications, Fixed Point Theory and Applications 2013 (2013) Article Number 6 21 pages.
- Z. S. Aliyev, Basic properties of fourth order differential operator with spectral parameter in the boundary condition, Central European Journal of Mathematics 8 (2) (2010) 378-388.
- M. L. Rasulov, Application of contour integral method (in Russian), Navka, Moskow, 1997.
- K. Aydemir, Boundary value problems with eigenvalue depending boundary and transmission conditions, Boundary Value Problems 2014 (2014) Article Number 131 11 pages.
- K. Aydemir, O. Sh. Mukhtarov, Specturm and Green’s function of a many interval Sturm-Liouville problem, Z. Naturforsch 70 (5) (2015) 301-308.
- M. Kadakal, O. Sh. Mukhtarov, Discontinuous Sturm-Liouville problems containing eigenparameter in the boundary conditions, Acta Mathematica Sinica 22 (5) (2006) 1519-1528.
- M. Kandemir, Irregular boundary value problems for elliptic differential-operator equations with discontinuous coefficients and transmission conditions, Kuwait Journal of Science and Engineering 39 (1) (2012) 71-97.
- M. A. Sadybekov, B. Kh. Turmetov, B. T. Torebek, Solvability of nonlocal boundary-value problems for the Laplace equation in the ball, Electronic Journal of Differential Equations 2014 (2014) Article Number 157 14 pages.
- T. Kato, Perturbation theory for linear operators, Classics in Mathematics, Sipringer-Verlag, New York, 1966.
- O. V. Besov, V. P. Il’in, S. M. Nikol’skii, Integral representation of functional and imbedding theorems, V. H. Winston, the University of Michigan, New York, 1978.
Yıl 2024,
Cilt: 13 Sayı: 3, 175 - 185, 31.12.2024
Öz
Proje Numarası
-
Kaynakça
- I. Titeux, Y. Yakubov, Comletenes of root functions for the thermal condition in a strip with piecewise continuous coefficients, Mathematical Models and Methods in Applied Sciences 7 (7) (1997) 1035-1050.
- M. Kandemir, O. Sh. Mukhtarov, Many point boundary value problems for elliptic differentialoperator equations with interior singularities, Mediterranean Journal of Mathematics 17 (2020) Article Number 35 21 pages.
- O. Muhtarov, S. Yakubov, Problems for ordinary differential equations with transmission conditions, Applicable Analysis 81 (2002) 1033-1064.
- M. Kandemir, O. Sh. Mukhtarov, Nonlocal Sturm-Liouville problems with integral terms in the boundary conditions, Electronic Journal of Differential Equations 2017 (2017) Article Number 11 12 pages.
- M. Kandemir, Y.Yakubov, Regular boundary value problems with a discontinuous coefficient, functional-multipoint conditions and a linear spectral parameter, Israel Journal of Mathematics 180 (1) (2010) 255-270.
- O. Sh. Mukhtarov, Discontinuous boundary value problem with spectral parameter in boundary conditions, Turkish Journal of Mathematics 18 2 (1994) 183-192.
- O. Sh. Mukhtarov, K. Aydemir, Eigenfunction expansion for Sturm-Liouville problems with transmission conditions at one interior point, Acta Mathematica Scientia 35 (3) (2015) 639-649.
- A. V. Likov, Y. A. Mikhailov, The theory of heat and mass transfer, Qosenergaizdat (Russian), 1963.
- M. Kandemir, O. Sh. Mukhtarov, Y. Yakubov, Irregular boundary value problems with discontinuous coefficients and the eigenvalue parameter, Mediterranean Journal of Mathematics 6 (2009) 317-338.
- M. S. Alves, J. E. M. Rivera, M. Sepulveda, O. V. Villagran,Transmission problem in thermoelasticity, Hindawi 2011 (2011) Article Number 190548 33 pages.
- M. S. Agranovich, Spectral properties of diffraction problems, in: N. N. Voitovich, B. Z. Kazenelenbaum, A. N. Sivov (Eds.), The Generalized Method of Eigenoscillations in the Theory of Diffraction, Nauka, Moscow, 1977 (in Russian: translated into English Wiley-VCH, Berlin 1999).
- A. Stikonas, The Sturm-Liouville problem with a nonlocal boundary condition Lithuanian Mathematical Journal, 47 (3) (2007) 336-351.
- H. Triebel, Interpolation theory function spaces differential operators, in: M. Artin, H. Bass, J. Eells, W. Feit, P. J. Freyd, F. W. Gehring, H. Halberstam, L. V, Hormander, M. Kac, J. H. B. Kemperxuan, H. A. Lauwerier, W. A. J. Luxemburg, F, P. Peterson, I. M. Singer, and A. C. Zaanen (Eds.), Vol. 18, Nort Holland, Amsterdam, 1978.
- S. Yakubov, Y. Yakubov, Differential-operator equation ordinary and partial differential equation, in: A. Jeffrey, H. Brezis, R. G. Douglas (Eds.), Monographs and Surveys in Pure and Applied Mathematics, 1st Edition, Chapman and Hall/CRC, Boca Raton London, 1999.
- N. S. Imanbaev, M. A. Sadybekov, Characteristic determinant of the spectral problem for the ordinary differential operator with the boundary load, in: A. Ashyralyev, E. Malkowsky (Eds.), International Conference on Analysis and Applied Mathematics, Shymkent, 2014 - AIP Conference Proceedings 1611 (1) (2014) 261-265.
- V. B. Shakhmurov, Linear and nonlinear abstract elliptic equations with VMO coefficients and applications, Fixed Point Theory and Applications 2013 (2013) Article Number 6 21 pages.
- Z. S. Aliyev, Basic properties of fourth order differential operator with spectral parameter in the boundary condition, Central European Journal of Mathematics 8 (2) (2010) 378-388.
- M. L. Rasulov, Application of contour integral method (in Russian), Navka, Moskow, 1997.
- K. Aydemir, Boundary value problems with eigenvalue depending boundary and transmission conditions, Boundary Value Problems 2014 (2014) Article Number 131 11 pages.
- K. Aydemir, O. Sh. Mukhtarov, Specturm and Green’s function of a many interval Sturm-Liouville problem, Z. Naturforsch 70 (5) (2015) 301-308.
- M. Kadakal, O. Sh. Mukhtarov, Discontinuous Sturm-Liouville problems containing eigenparameter in the boundary conditions, Acta Mathematica Sinica 22 (5) (2006) 1519-1528.
- M. Kandemir, Irregular boundary value problems for elliptic differential-operator equations with discontinuous coefficients and transmission conditions, Kuwait Journal of Science and Engineering 39 (1) (2012) 71-97.
- M. A. Sadybekov, B. Kh. Turmetov, B. T. Torebek, Solvability of nonlocal boundary-value problems for the Laplace equation in the ball, Electronic Journal of Differential Equations 2014 (2014) Article Number 157 14 pages.
- T. Kato, Perturbation theory for linear operators, Classics in Mathematics, Sipringer-Verlag, New York, 1966.
- O. V. Besov, V. P. Il’in, S. M. Nikol’skii, Integral representation of functional and imbedding theorems, V. H. Winston, the University of Michigan, New York, 1978.
Toplam 25 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Adi Diferansiyel Denklemler, Fark Denklemleri ve Dinamik Sistemler |
| Bölüm | Articles |
| Yazarlar | |
| Proje Numarası | - |
| Yayımlanma Tarihi | 31 Aralık 2024 |
| Gönderilme Tarihi | 22 Ağustos 2024 |
| Kabul Tarihi | 10 Ekim 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 13 Sayı: 3 |
