The paper presents a brief overview of the main areas of research and educational activities of the founder of the Irkutsk school on the theory of differential operator equations with the irreversible operator in the main part, the professor of the Institute of Mathematics and Information Technologies of Irkutsk State University N. A. Sidorov.

Mihail Falaleev, Dr. Sci. (Phys.–Math.), Prof., Irkutsk State University, 1, K. Marx st., Irkutsk, 664003, Russian Federation, tel.: (3952)521296, email: mihail@ic.isu.ru

Olga Romanova, Cand. Sci. (Phys.–Math.), Irkutsk State University, 1, K. Marx st., Irkutsk, 664003, Russian Federation, tel.: (3952)521298, email: olga@baikal.ru

Alekandr Sinitsyn, Dr. Sci. (Phys.–Math.), Prof., Universidad Nacional de Colombia, Bogota D.C., Colombia, e-mail: avsinitsyn@yahoo.com

Alena Dreglea, Cand. Sci. (Phys.–Math.), Assoc. Prof., Irkutsk National Research Technical University, 83, Lermontov st., Irkutsk, 664074, Russian Federation, tel.: (3952)998440, email: adreglea@gmail.com

Roman Leont’ev, Cand. Sci. (Phys.–Math.), Assoc. Prof., Irkutsk State University, 1, K. Marx st., Irkutsk, 664003, Russian Federation, tel.: (3952)521298, email: romallisu@gmail.com

Denis Sidorov, Dr. Sci. (Phys.–Math.), Prof. RAS, Principal Researcher, Melentiev Energy Systems Institute SB RAS, 130, Lermontov st., Irkutsk, 664033, Russian Federation, tel. (+7) 500 646 ext. 258; Irkutsk State University, 1, K. Marx st., Irkutsk, 664003, Russian Federation; Irkutsk National Research Technical University, 83, Lermontov st., Irkutsk, 664074, Russian Federation, e-mail: dsidorov@isem.irk.ru

Falaleev M. V., Romanova O. A., Sinitsyn A. V., Dreglea A. I., Leont’ev R. Ju., Sidorov D. N. On the Occasion of the 80th Birthday of Professor N. A. Sidorov. The Bulletin of Irkutsk State University. Series Mathematics, 2020, vol. 32, pp. 134-143. (in Russian) https://doi.org/10.26516/1997-7670.2020.32.134

1. Scientific schools of Irkutsk State University, 1918–2018. Issue 2. Mathematical Sciences. Irkutsk, ISU Publ., 2019, 115 p. (in Russian)
2. Sidorov N.A., Sidorov D.N., Li Y. Areas of Attraction of Equilibrium Points of Nonlinear Systems: Stability, Branching and Blow-up of Solutions. The Bulletin of Irkutsk State University. Series Mathematics, 2018, vol. 23, pp. 46-63. (In Russian). https://doi.org/10.26516/1997-7670.2018.23.46
3. Sidorov N.A., Sidorov D.N. On Successive Approximations of Solutions of a Singular Cauchy Problem. Trudy Inst. Math. i Mekh. UrO RAN, 2012, vol. 18, no 2, pp. 238–244. (in Russian).
4. Sidorov N.A., Dreglea A.I. The Identification of External Force Dynamics in the Modeling of Vibration. The Bulletin of Irkutsk State University. Series Mathematics, 2017, vol. 19, pp. 105-112. (in Russian) https://doi.org/10.26516/1997-7670.2017.19.105
5. Sidorov D.N., Sidorov N.A. Research methods for a class of Volterra integral equations of the first kind with piecewise defined operator kernels [Metody issledovaniya odnogo klassa integral’nykh uravneniy vol’terry I roda s kusochnoopredelennymi operatornymi yadram] Proceedings of the XII Conference on control problems of VSPU-2014. V.A. Trapeznikov Institute of Control Sciences RAS, 2014, pp. 745-756.
6. Dreglea A.I., Sidorov N.A. Integral equations in identification of external force and heat source density dynamics. Buletinul Academiei de Stiinte a Republicii Moldova. Matematica, 2018, vol. 88, no. 3, pp. 68-77.
7. Dreglea A.I., Sidorov N.A. The structure of solutions of systems of nonlinear integral equations with functional perturbation argument. Lomonosov readings in Altai: fundamental problems of science and education, 2017, pp. 257-260. (In Russian).
8. Dreglea A.I., Sidorov N.A. Identification of dynamics of external force change in modeling of oscillations of strings with fixed ends. Analytical and numerical methods for modeling natural-scientific and social problems: materials. All-Russia Conference. Penza, 2016. (In Russian).
9. Muftahov I.R., Sidorov D.N., Sidorov N.A. On perturbation method for the first kind equations: regularization and application. Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software, 2015, vol. 8, no. 2, pp. 69–80.
10. Sidorov N.A., Sidorov D.N., Muftahov I.R. Perturbation theory and the Banach–Steinhaus theorem for regularization of the linear equations of the first kind. The Bulletin of Irkutsk State University. Series Mathematics, 2015, vol. 14, pp. 82-99.
11. Rendon L., Sinitsyn A.V., Sidorov N.A. Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov-Maxwell system. Revista Colombiana de Matematicas, 2016, vol. 50, no. 1, pp. 85-107.
12. Noeiaghdam S., Sidorov D., Sizikov V., Sidorov N. Control of accuracy on Taylorcollocation method to solve the weakly regular Volterra integral equations of the first kind by using the CESTAC method. Applied and Computational Mathematics, 2020, vol. 19, no. 1, pp. 87-105.
13. Rojas E.M., Sidorov N.A., Sinitsyn A.V. A boundary value problem for noninsulated magnetic regime in a vacuum diode. Symmetry, 2020, vol.12, no. 4, p. 617. https://doi.org/10.3390/sym12040617
14. Sidorov N.A., Sidorov D.N., Dreglea A.I. Solvability and bifurcation of solutions of nonlinear equations with Fredholm operator. Symmetry, 2020, vol. 12 (to appear)
15. Sidorov N.A., Sidorov D.N., Sinitsyn A.V. Toward General Theory of Differential Operator and Kinetic Models. Book Series: World Scientific Series on Nonlinear Science Series A, vol. 97, eds. Prof. L. Chua. S’pore, World Scientific, 2020, 400 p. https://doi.org/10.1142/11651
16. Sidorov N.A., Sidorov D.N., Li Y. Nonlinear systems’ equilibrium points: branching, blow-up and stability. Journal of Physics: Conference Series, 2019, no. 1268, p. 012065.
17. Sidorov N.A., Sidorov D.N., Li Y. Basins of attraction and stability of nonlinear systems equilibrium points. Differential Equations and Dynamical Systems, Springer, 2019, pp. 1-10.
18. Sidorov N.A. Classic Solutions of Boundary Value Problems for Partial Differential Equations with Operator of Finite Index in the Main Part of Equation. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 27, pp. 55-70. https://doi.org/10.26516/1997-7670.2019.27.55
19. Sidorov D.N., Sidorov N.A. Solution of irregular systems of partial differential equations using skeleton decomposition of linear operators. Bulletin of the South Ural State University, Series Mathematical Modelling, Programming and Computer Software, 2017, vol. 10, no. 2. pp. 63–71. https://doi.org/10.14529/mmp170205
20. Sidorov N.A., Sidorov D.N. On the solvability of a class of Volterra operator equations of the first kind with piecewise continuous kernels. Mathematical Notes, 2014, vol. 96, no. 5-6, pp. 811-826.
21. Sidorov N.A. Bifurcation points of nonlinear operators: existence theorems, asymptotics and application to the Vlasov–Maxwell system. The Bulletin of Irkutsk State University. Series Mathematics, 2013, vol. 6, no. 4. pp. 85-106.
22. Sidorov N.A., Leont’ev R.Y., Dreglya A.I. On small solutions of nonlinear equations with vector parameter in sectorial neighborhoods. Mathematical Notes, 2012, vol. 91, no. 1-2, pp. 90-104. https://doi.org/10.1134/S0001434612010105
23. Sidorov N.A., Sidorov D.N., Leont’ev R.Y. Successive approximations to the solutions to nonlinear equations with a vector parameter in a nonregular case. Journal of Applied and Industrial Mathematics, 2012, vol. 6, no. 3, pp. 387-392.
24. Sidorov D.N., Sidorov N.A. Convex majorants method in the theory of nonlinear Volterra equations. Banach J. Math. Anal, 2012, vol. 6, no. 1, pp. 1–10.
25. Sidorov N.A., Falaleev M.V. Continuous and generalized solutions of singular integro-differential equations in Banach spaces. Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software, 2012, vol. 264, no. 5, pp. 62-74.