01.01.02 (Differential equations, dynamical systems, and optimal control)
differential equations; integral equations; integro-differential equations; equations in partial derivatives; asymptotical methods; classes of singular-perturbed equations and systems; periodical and nearly periodical solutions; incorrect problems; uniqueness, existence and stability; existence and approximation of generalized integral equations.
Has shown the principal difference of integro-differential equations by perturbation theory under derivatives of corespondent theory of differential equations and created general asymptotical method for searching of wide class of singular-perturbed equations and systems. Developed the theory of branching of periodical, nearly periodical and bounded solutions of differential and integro-differential perturbed equations under highest derivative. Developed the theory of linear and nonlinear integral equations of first class of equations in continuous on final interval space, offered the methods of regularization of solutions of these equations, based on methods of theory of singular-perturbed systems. Developed the method of additional argument, the main idea of which is that the initial problem by inserting the additional variable is reduced to convenient to searching system of integral equations.
Graduated from Faculty of Physics and Mathematics of Kyrgyz State University (KSU) in 1953. Ph.D. thesis was defended in 1957. D.Sc. Thesis was defended in 1965. A list of my works contains more than 200 titles. Since 1966 I have led the research seminar of mathematicians at the Institute of Mathematics of National Academy of Sciences.
Member of Academy of Sciences of Kyrgyz Republic since 1979. Member-Correspondent of Russian Academy of Sciences, Russian Federation since 1981. I was awarded the Order of Red Labor in 1981, Order of Manas in 1999. Honorable Gold Medal of President of Kyrgyz Republic for distinguished scientific achievements in XX century in 2001.
Asymptotical Methods in Theory of singular-perturbed integer-differential systems, Ilim, Frunze, 1972.
Oscillations and stability of solution of singular-perturbed integer-differential systems, Ilim, Frunze, 1974.