Third-order boundary value transmission problems

In this paper, we consider some third-order operators with transmission conditions. In particular, it is shownthat such operators are formally symmetric in the corresponding Hilbert spaces and we introduce the resolvent operatorsassociated with the differential operators. After showing that the eigenvalues of the problems are real and discrete weintroduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of data.

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[1] Akdoğan Z, Demirci M, Mukhtarov OSh. Green function of discontinuous boundary-value problem with transmission conditions. Mathematical Methods in the Applied Sciences 2007; 30: 1719-1738.
[2] Aydemir K, Mukhtarov OSh. Spectrum and Green’s function of a many-interval Sturm-Liouville problem. Zeitschrift für Naturforschung A 2015; 70: 301-308.
[3] Dieudonne J. Foundations of Modern Analysis. New York, NY, USA: Academic Press, 1969.
[4] Kong Q, Zettl A. Linear ordinary differential equations in “inequalities and applications”. In: Agarwal RP (editor). Vol. 3 - Inequalities and Applications. Singapore, World Scientific, 1994, pp. 381-397.
[5] Mukhtarov OSh, Aydemir K. New type of Sturm-Liouville problems in associated Hilbert spaces. Journal of Function Spaces 2014; 2014: 606815. doi: http://dx.doi.org/10.1155/2014/606815
[6] Mukhtarov OSh, Olgar H, Aydemir K. Resolvent operator and spectrum of new type boundary value problems. Filomat 2015; 29: 1671-1680.
[7] Mukhtarov OSh, Olgar H, Aydemir K, Jabbarov I. Operator-pencil realization of one Sturm-Liouville problem with transmission conditions. Applied and Computational Mathematics 2018; 17: 284-294.
[8] Uğurlu E. Regular third-order boundary value problems. Applied Mathematics and Computations 2019; 343: 247-257.

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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