Boundedly solvable neutral type delay differential operators of the first order
Eurasian mathematical journal, Tome 10 (2019) no. 3, pp. 20-27.

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In this work, by using methods of operator theory, all boundedly solvable extensions of the minimal operator generated by a linear neutral type delay differential-operator expression of the first order in a Hilbert space of vector-functions on a finite interval are described. Furthermore, the geometry of spectrum sets of these operators is studied.
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Z. I. Ismailov; P. Ipek Al. Boundedly solvable neutral type delay differential operators of the first order. Eurasian mathematical journal, Tome 10 (2019) no. 3, pp. 20-27. http://geodesic.mathdoc.fr/item/EMJ_2019_10_3_a1/

[1] N. A. Allen, Computational software for building biochemical reaction network models with differential equations, PhD Dissertation, Faculty of the Virginia Polytechnic Institute and State University, 2005, 119 pp.

[2] Ch. T. H. Baker, G. A. Bocharov, F. A. Rihan, Neutral delay differential equations in the modelling of cell growth, Applied Mathematics Group, Researc Report, Department of Mathematics, University of Chester, 30 pp.

[3] K. Bareli, R. M. Noyes, “Gas-evolution oscillators, A model based on a delay equation”, J. Phys. Chem., 96 (1992), 7664–7670

[4] A. Brown, C. Pearcy, “Spectra of tensor product of operators”, Proc. Amer. Math. Soc., 17:1 (1966), 162–166 | MR | Zbl

[5] T. Chevalier, A. Freund, J. Ross, “The effects of a nonlinear delayed feedback on a chemical reaction”, J. Chem. Phys., 95 (1991), 308–316

[6] I. R. Epstein, “Delay effects and differential delay equations in chemical-kinetics”, International Reviews in Physical Chemistry, 11:1 (1992), 135–160 | MR

[7] I. R. Epstein, Y. Luo, “Differential delay equation in chemical kinetics, Nonlinear models: The cross-shaped phase diagram and the oregonator”, J. Chem. Phys., 95 (1991), 244–254

[8] E. L. Haseltine, J. B. Rawlings, “Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics”, J. Chem. Phys., 117:15 (2002), 6959–6969

[9] L. Hörmander, “On the theory of general partial differential operators”, Acta Math., 94 (1955), 161–248 | MR | Zbl

[10] Z. I. Ismailov, P. Ipek, “Spectrums of solvable pantograph differential-operator for first order”, Abstract and Applied Analysis, 2014, 1–8 | MR

[11] B. K. Kokebaev, M. Otelbaev, A. N. Shynybekov, “On the theory of contraction and extension of operators I”, Izv. Akad. Nauk Kazakh. SSR Ser. Fiz. Mat., 5 (1982), 24–26 (in Russian) | MR | Zbl

[12] B. K. Kokebaev, M. Otelbaev, A. N. Shynybekov, “On questions of extension and restriction of operator”, Soviet Math. Dokl., 28:1 (1983), 259–262 (English Translation) | MR | Zbl

[13] B. K. Kokebaev, M. Otelbaev, A. N. Shynybekov, “On the theory of contraction and extension of operators II”, Izv. Akad. Nauk Kazakh. SSR Ser. Fiz. Mat., 110 (1983), 24–26 (in Russian) | MR | Zbl

[14] M. Otelbaev, A. N. Shynybekov, “Well-posed problems of Bitsadze-Samarskii type”, Soviet Math. Dokl., 26:1 (1983), 157–161 (English Translation) | MR

[15] B. Shi, “Asymptotic behavior of solutions for a delay reaction-diffusion equation of neutral type”, Nikonkai Math. J., 13 (2002), 133–143 | MR | Zbl

[16] M. I. Vishik, “On general boundary problems for elliptic differential equations”, Amer. Math. Soc. Transl. II, 24 (1963), 107–172 | MR | Zbl

[17] J. Weiner, F. W. Schneider, K. Bar-Eli, “Delayed-output-controlled chemical oscillations”, J. Phys. Chem., 93 (1989), 2704–2711