BibTex RIS Kaynak Göster

Delay differential operators and some solvable models in life sciences

Yıl 2017, Cilt: 66 Sayı: 2, 91 - 99, 01.08.2017
https://doi.org/10.1501/Commua1_0000000804

Öz

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

Kaynakça

  • 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: ipekpembe@gmail.com Current address, B. Yilmaz: Marmara University, Department of Mathematics, Kadıköy, , Istanbul, Turkey E-mail address, B. Yilmaz: bulentyilmaz@marmara.edu.tr Current address, Z. I. Ismailov: Karadeniz Technical University, Department of Mathematics, , Trabzon, Turkey E-mail address, Z. I. Ismailov: zameddin.ismailov@gmail.com
Yıl 2017, Cilt: 66 Sayı: 2, 91 - 99, 01.08.2017
https://doi.org/10.1501/Commua1_0000000804

Öz

Kaynakça

  • 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: ipekpembe@gmail.com Current address, B. Yilmaz: Marmara University, Department of Mathematics, Kadıköy, , Istanbul, Turkey E-mail address, B. Yilmaz: bulentyilmaz@marmara.edu.tr Current address, Z. I. Ismailov: Karadeniz Technical University, Department of Mathematics, , Trabzon, Turkey E-mail address, Z. I. Ismailov: zameddin.ismailov@gmail.com
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

P. Ipek Bu kişi benim

B. Yılmaz Bu kişi benim

İ. Ismaılov Z. Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 66 Sayı: 2

Kaynak Göster

APA Ipek, P., Yılmaz, B., & Ismaılov Z., İ. (2017). Delay differential operators and some solvable models in life sciences. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 91-99. https://doi.org/10.1501/Commua1_0000000804
AMA Ipek P, Yılmaz B, Ismaılov Z. İ. Delay differential operators and some solvable models in life sciences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Ağustos 2017;66(2):91-99. doi:10.1501/Commua1_0000000804
Chicago Ipek, P., B. Yılmaz, ve İ. Ismaılov Z. “Delay Differential Operators and Some Solvable Models in Life Sciences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, sy. 2 (Ağustos 2017): 91-99. https://doi.org/10.1501/Commua1_0000000804.
EndNote Ipek P, Yılmaz B, Ismaılov Z. İ (01 Ağustos 2017) Delay differential operators and some solvable models in life sciences. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 91–99.
IEEE P. Ipek, B. Yılmaz, ve İ. Ismaılov Z., “Delay differential operators and some solvable models in life sciences”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 66, sy. 2, ss. 91–99, 2017, doi: 10.1501/Commua1_0000000804.
ISNAD Ipek, P. vd. “Delay Differential Operators and Some Solvable Models in Life Sciences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (Ağustos 2017), 91-99. https://doi.org/10.1501/Commua1_0000000804.
JAMA Ipek P, Yılmaz B, Ismaılov Z. İ. Delay differential operators and some solvable models in life sciences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:91–99.
MLA Ipek, P. vd. “Delay Differential Operators and Some Solvable Models in Life Sciences”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 66, sy. 2, 2017, ss. 91-99, doi:10.1501/Commua1_0000000804.
Vancouver Ipek P, Yılmaz B, Ismaılov Z. İ. Delay differential operators and some solvable models in life sciences. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):91-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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