Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
12.01.1937
E-mail: ,
Website: https://www.rmi.acnet.ge/~kig Keywords: boundary value problems for ordinary differential equations and systems; periodic and bounded solutions; asymptotic of solutions of nonautonomous differential equations; oscillation theory.
Subject:
A method of a priori estimates of solutions of one-sided differential inequalities has been developed, on the basis of which the theory of boundary value problems of Cauchy–Nicoletti, Vallee Poussin, Kneser and periodic type has been constructed for ordinary differential equations and systems with nonintegrable singularities. Optimal existence and uniqueness criteria of periodic and bounded solutions have been established for higher order nonautonomous differential equations. A complete investigation has been carried out of asymptotic properties of solutions of a wide class of nonautonomous differential equations. In particular, the problem on the dimension of the space of vanishing at infinity solutions of a linear homogeneous equation of an arbitrary order has been solved; asymptotic formulas have been obtained for solutions of linear and quasilinear equations; necessary and sufficient conditions have been found for essentially nonlinear equations to have proper, singular, oscillatory and monotone solutions of various types, and asymptotic estimates of these solutions have been established.
Main publications:
Kiguradze I. T., Chanturia T. A. Asymptotic properties of solutions of nonaotonomous ordinary differential equations. Kluwer Academic Publishers, Dordrecht–Boston–London, 1993.
Kiguradze I. On periodic solutions of n-th order ordinary differential equations // Nonlinear Anal., 2000, 40(1–8), 309–321.
Kiguradze I., Kusano T. On periodic solutions of even-order ordinary differential equations // Ann. Mat. Pura Appl., 2001, 180(3), 285–301.
