Acceso abierto

The Resolvent of Impulsive Singular Hahn–Sturm–Liouville Operators


Cite

B.P. Allahverdiev and H. Tuna, A representation of the resolvent operator of singular Hahn–Sturm–Liouville problem, Numer. Funct. Anal. Optim. 41 (2020), no. 4, 413–431. Search in Google Scholar

R.Kh. Amirov and A.S. Ozkan, Discontinuous Sturm–Liouville problems with eigenvalue dependent boundary condition, Math. Phys. Anal. Geom. 17 (2014), no. 3–4, 483–491. Search in Google Scholar

M.H. Annaby, A.E. Hamza, and K.A. Aldwoah, Hahn difference operator and associated Jackson–Nörlund integrals, J. Optim. Theory Appl. 154 (2012), no. 1, 133–153. Search in Google Scholar

M.H. Annaby, A.E. Hamza, and S.D. Makharesh, A Sturm–Liouville theory for Hahn difference operator, in: M.Z. Nashed and X. Li (Eds.), Frontiers in Orthogonal Polynomials and q-Series, World Scientific, Singapore, 2018, pp. 35–83. Search in Google Scholar

M.H. Annaby, Z.S. Mansour, and I.A. Soliman, q-Titchmarsh–Weyl theory: series expansion, Nagoya Math. J. 205 (2012), 67–118. Search in Google Scholar

K. Aydemir, H. Olğar, and O.Sh. Mukhtarov, The principal eigenvalue and the principal eigenfunction of a boundary-value-transmission problem, Turk. J. Math. Comput. Sci. 11 (2019), no. 2, 97–100. Search in Google Scholar

K. Aydemir, H. Olğar, O.Sh. Mukhtarov, and F. Muhtarov, Differential operator equations with interface conditions in modified direct sum spaces, Filomat 32 (2018), no. 3, 921–931. Search in Google Scholar

F.A. Çetinkaya, A discontinuous q-fractional boundary value problem with eigenparameter dependent boundary conditions, Miskolc Math. Notes 20 (2019), no. 2, 795–806. Search in Google Scholar

Y. Guldu, R.Kh. Amirov, and N. Topsakal, On impulsive Sturm–Liouville operators with singularity and spectral parameter in boundary conditions, Ukrainian Math. J. 64 (2013), no. 12, 1816–1838. Search in Google Scholar

W. Hahn, Beitraäge zur Theorie der Heineschen Reihen. Die 24 Integrale der hyper-geometrischen q-Differenzengleichung. Das q-Analogon der Laplace–Transformation, Math. Nachr. 2 (1949), 340–379. Search in Google Scholar

W. Hahn, Ein Beitrag zur Theorie der Orthogonalpolynome, Monatsh. Math. 95 (1983), no. 1, 19–24. Search in Google Scholar

D. Karahan, On a q-analogue of the Sturm–Liouville operator with discontinuity conditions, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki 26 (2022), no. 3, 407–418. Search in Google Scholar

D. Karahan and Kh.R. Mamedov, Sampling theory associated with q-Sturm–Liouville operator with discontinuity conditions, J. Contemp. Appl. Math. 10 (2020), no. 2, 40–48. Search in Google Scholar

D. Karahan and Kh.R. Mamedov, On a q-boundary value problem with discontinuity conditions, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz. 13 (2021), no. 4, 5–12. Search in Google Scholar

A.N. Kolmogorov and S.V. Fomin, Introductory Real Analysis, Dover Publications, New York, 1970. Search in Google Scholar

B.M. Levitan and I.S. Sargsjan, Sturm–Liouville and Dirac Operators, Math. Appl. (Soviet Ser.), 59, Kluwer Academic Publishers Group, Dordrecht, 1991. Search in Google Scholar

A.V. Likov and Yu.A. Mikhailov, The Theory of Heat and Mass Transfer (in Russian), Qosenerqoizdat, 1963. Search in Google Scholar

S. Mosazadeh, Spectral properties and a Parseval’s equality in the singular case for q-Dirac problem, Adv. Difference Equ. (2019), Paper No. 522, 14 pp. DOI: 10.1186/s13662-019-2464-y. Search in Google Scholar

O. Mukhtarov, H. Olˇgar, and K. Aydemir, Eigenvalue problems with interface conditions, Konuralp J. Math. 8 (2020), no. 2, 284–286. Search in Google Scholar

M.A. Naimark, Linear Differential Operators, 2nd ed., Izdat. Nauka, Moscow, 1969; English transl. of 1st. ed., 1,2, New York, 1968. Search in Google Scholar

N. Palamut Kosar, On a spectral theory of singular Hahn difference equation of a Sturm–Liouville type problem with transmission conditions, Math. Methods Appl. Sci. 46 (2023), no. 9, 11099–11111. Search in Google Scholar

E.C. Titchmarsh, Eigenfunction Expansions Associated with Second-order Differential Equations, Part I, Clarendon Press, Oxford, 1962. Search in Google Scholar

Y.P. Wang and H. Koyunbakan, On the Hochstadt–Lieberman theorem for discontinuous boundary-valued problems, Acta Math. Sin. (Engl. Ser.) 30 (2014), no. 6, 985–992. Search in Google Scholar

H. Weyl, Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Functionen, Math. Ann. 68 (1910), no. 2, 220–269. Search in Google Scholar

eISSN:
2391-4238
Idioma:
Inglés
Calendario de la edición:
2 veces al año
Temas de la revista:
Mathematics, General Mathematics