Contents • • • • • • • • • • • • • • • • • • • • Biography [ ] Early life (1909–1921) [ ] Nikolay Bogolyubov was born on 21 August 1909 in, to and teacher of, and Nikolay Mikhaylovich Bogolyubov, and Olga Nikolayevna Bogolyubova, a teacher of music. The Bogolyubovs relocated to the village of Velikaya Krucha in the (now in, ) in 1919, where the young Nikolay Bogolyubov began to study physics and mathematics. The family soon moved to in 1921, where they continued to live in poverty as the elder Nikolay Bogolyubov only found a position as a priest in 1923. He attended research seminars in and soon started to work under the supervision of the well-known contemporary mathematician. In 1924, at the age of 15, Nikolay Bogolyubov wrote his first published scientific paper On the behavior of solutions of linear differential equations at infinity. In 1925 he entered Ph.D. Program at the Academy of Sciences of the and obtained the degree of ( Candidate of Sciences, equivalent to a Ph.D.) in 1928, at the age of 19, with the doctoral thesis titled On direct methods of variational calculus.

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In 1930, at the age of 21, he obtained the degree of ( Doctor of Sciences, equivalent to ), the highest degree in the Soviet Union, which requires the recipient to have made a significant independent contribution to his or her scientific field. This early period of Bogolyubov's work in science was concerned with such mathematical problems as direct methods of the, the theory of, methods of approximate solution of,. This earlier research had already earned him recognition. Serial tendering advantages and disadvantages. One of his essays was awarded the Prize in 1930, and the author was awarded the erudite degree of doctor of mathematics. This was the period when the scientific career of the young Nikolai Bogolyubov began, later producing new scientific trends in modern mathematics, physics, and mechanics. Since 1931, Krylov and Bogolyubov worked together on the problems of nonlinear mechanics and nonlinear oscillations.

They were the key figures in the 'Kiev school of nonlinear oscillation research', where their cooperation resulted in the paper ' On the quasiperiodic solutions of the equations of nonlinear mechanics' (1934) and the book Introduction to Nonlinear Mechanics (1937; translated to English in 1947) leading to a creation of a large field of non-linear mechanics. And this can explain, as the authors believe, the need to shape the collection of problems of non-linear perturbation theory into a special science, which could be named NON-LINEAR MECHANICS. Krylov and N. Bogolyubov, New methods in non-linear mechanics, ONTI GTTI, Moscow-Leningrad, 1934 Distinctive features of the Kiev School approach included an emphasis on the computation of solutions (not just a proof of its existence), approximations of periodic solutions, use of the invariant manifolds in the phase space, and applications of a single unified approach to many different problems. From a point of view, the key achievement of the Kiev School was the development by Krylov and Bogolyubov of the method for the analysis of nonlinear control problems.