Delay differential operators and some solvable models in life sciences

Year 2017, Volume: 66 Issue: 2, 91 - 99, 01.08.2017

P. Ipek B. Yılmaz İ. Ismaılov Z.

https://doi.org/10.1501/Commua1_0000000804

Cited By: 2

Abstract

Using the methods of the spectral theory of differential operators in Hilbert spaces L2-solvability of some models arising in mathematical biology are investigated. Particularly, concrete solvable models are given

Keywords

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References

• Bellman, R. and Cooke, K.L., Diğerential-Diğerence Equations, United State Air Force Project Rand, (1963).
• Britton, N.F., Essentual Mathematical Biology, Springer,(2003).
• Dezin, A. General Problems in the Theory of Boundary Value Problems, Nauka, Moskow, (1980).
• Edelstein-Keshet, L., Mathematical Models in Biology. McGraw-Hill, New York, (1988).
• Erneux, T., An Introduction to Delay Diğerential Equations with Applications to the Life Sciences, Springer, Verlag, (2011).
• Hale, J.K. and Lunel, S.M.V, Introduction to Functional Diğerential Equations, Springer, (1993).
• Ismailov, Z.I., Guler, B.O. and Ipek P., Solvability of First Order Functional Diğerential Operators, Journal of Mathematical Chemistry, 53(2015), 2065-2077.
• Ismailov, Z.I., Guler, B.O. and Ipek P., Solvable Time-Delay Diğerential Operators for First and Their Spectrum, Hacettepe Journal of Mathematics and Statistic, vol.45, pp.755-764, Ismailov, Z.I. and Ipek, P., Spectrums of Solvable Pantograph Diğerential Operators for First Order, Abstract and Applied Analysis,2014(2014), 1-8.
• Ismailov, Z.I. and Ipek, P., Solvability of Multipoint Diğerential Operators of First Order Electronic Journal of Diğerential Equations 2015(2015), 1-10.
• Ismailov, Z.I. and Ipek P., Boundedly Solvable Multipoint Diğerential Operators of First Order on Right Semi-Axis, AIP, (2015), 1-5.
• Ismailov, Z.I. and Ipek, P., Structure of Spectrum of Solvable Delay Diğerential Operators for First Order, Journal of Analysis and Number Theory, 7(2015),1-7.
• Ismailov, Z.I. and Ipek, P., Comptational Analysis„ AMAT, Ankara, May 2015, Selected
• Contributions, Spring, p.299-311, 2016.
• Ismailov, Z.I., Otkun Çevik, E., Guler, B.O. and Ipek, P., Structure Of Spectrum of Solv- able Pantograph Diğerential Operators for the First Order, AIP Conference Proceedings, (2014), 89-94.
• Karakaya, V. and Altun, M., Fine Spectra of Upper Triangular Double-Band Matrices, J. Comp. Appl. Math., 234(2010), 1387-1394.
• Rofe-Beketov, F.S. and Kholkin, A.M., Spectral Analysis of Diğerential Operators, World Scienti…c Monograph Series in Mathematics, 7, World Scienti…c Publishing Co. Pte. Ltd., Hanckensack, NJ, (2005).
• Ruan, S., Delay Diğerential Equations in Single Species Dynamics, In: Delay diğerential equations and applications, Springer, Berlin, (2006), 477-517.
• Smith, H., Applied Delay Diğerential Equations, Springer, Verlag, (2009).
• Villasana, M. and Radunskaya, A., A Delay Diğerential Equation Model for Tumor Growth, J. Math. Biol., 47(2003), 270-294.
• Vishik, M.I., On Linear Boundary Problems for Diğerential Equations, Doklady Akad. Nauk SSSR (N.S) 65(1949), 785-788
• Vishik, M.I., On General Boundary Problems for Elliptic Diğerential Equations, Amer. Math. Soc. Transl. II 24(1963), 107-172
• Yilmaz, B., Ismailov, Z.I., Bounded Solvability of Mixed-Type Functional Diğerential Oper- ators for First Order, Electronic Journal of Diğerential Equation, vol.2016, pp. 1-8, 2016.
• Current address, P. Ipek: Karadeniz Technical University, Institute of Natural Sciences, 61080, Trabzon, Turkey
• E-mail address, P. Ipek: [e-mail] Current address, B. Yilmaz: Marmara University, Department of Mathematics, Kadıköy, , Istanbul, Turkey E-mail address, B. Yilmaz: [e-mail] Current address, Z. I. Ismailov: Karadeniz Technical University, Department of Mathematics, , Trabzon, Turkey E-mail address, Z. I. Ismailov: [e-mail]