The brief review of monograph [Sidorov N., Sidorov D., Sinitsyn A. 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, World Scientific, Singapore, London, 2020] is provided. This monograph devoted to the state-ofthe-art methods for the non-standard classes of differential operator and kinetic equations from a constructive point of view. In addition to the qualitative problems associated with the proof of existence theorems, bifurcation and blow-up of solutions of nonlinear systems, this monograph provides the formulations of the novel initial-boundary value problems in function spaces. Attention is paid to the problem of constructing asymptotic approximations of solutions and numerical-analytical analysis in mathematical modeling.

Nikolai Sidorov, Dr. Sci. (Phys.–Math.), Prof., Irkutsk State University, 1, K. Marx st., Irkutsk, 664003, Russian Federation, e-mail: sidorov@isu.runnet.ru

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

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

Sidorov N. A., Sidorov D. N., Sinitsyn A. V. Review of Monograph “Toward General Theory of Differential-Operator and Kinetic Models”. The Bulletin of Irkutsk State University. Series Mathematics, 2020, vol. 32, pp. 118-123. (in Russian) https://doi.org/10.26516/1997-7670.2020.32.118

1. Sidorov N., Sidorov D., Sinitsyn A. 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
2. Sidorov N., Loginov B., Sinitsyn A. and Falaleev M. Lyapunov-Schmidt Methods in Nonlinear Analysis and Applications. Book Series: Mathematics and Its Applications, vol. 550. Kluwer, 2002, 548 p. https://doi.org/10.1007/978-94-017-2122-6
3. Sidorov D. Integral Dynamical Models: Singularities, Signals & Control. Book Series: World Scientific Series on Nonlinear Science Series A, vol. 87. S’pore, World Scientific, 2015, 300 p. https://doi.org/10.1142/9278