Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
30.09.1933
E-mail: ,
Keywords: the method of guiding functions in the theory of nonlinear oscillations; stability in critical cases; matrix equations of Liapounov and Rikkatti; periodic optimization.
Subject:
The guiding functions method of approving the uniqueness theorems and of obtaining the estimates of periodical, almost periodical and bounded solutions of nonlinear systems of ordinary differential equations was developed together with M. A. Krasnoselskii.The formulas of the norm and logarithmic norm of the linear operator (matrix) on the subspace were obtained for the case where the norm of the vector is defined as the maximum of the absolute values of its coordinates. The proof of the stabilizing solvability theorem for the discrete matrix Lourie (Riccati) equation based on the methods of the cone theory was obtained, that gives the new proof of the discrete matrix Kalman–Popov–Yakubovitch theorem. The position and the meaning of different inequalities (Wirtinger, Steklov, Bohr–Favard, Bernstein, Stechkin, Nikolskii etc.) for smooth periodical functions in the theory of nonlinear oscillations is demonstrated.
Main publications:
Krasnoselskii M. A., Perov A. I. Ob odnom printsipe suschestvovaniya ogranichennykh, periodicheskikh i pochti-periodicheskikh reshenii u sistemy obyknovennykh differentsialnykh uravnenii // DAN SSSR, 1958, 123, # 2, 235–238.
Krasnoselskii M. A., Perov A. I., Povolotskii A. I., Zabreiko P. P. Vektornye polya na ploskosti. Moskva. Fizmatgiz. 1963. 248 s.
Perov A. I. Variatsionnye metody v teorii nelineinykh kolebanii. Voronezh. Izd-vo VGU. 1981. 196 s.
Trubnikov Yu. V., Perov A. I. Differentsialnye uravneniya s monotonnymi nelineinostyami. Minsk. Nauka i tekhnika. 1986. 200 s.
Perov A. I. Formuly dlya normy lineinogo operatora na podprostranstve // DAN, 1999, 368, # 5, 601–603.
