Differential equations, control, stability, systems with delays, mathematical modelling.
Main publications:
A. B. Kim, Pryamoi metod Lyapunova v teorii ustoichivosti sistem s posledeistviem, Uralskii gosuniversitet, Ekaterinburg, 1992
A. B. Kim, $i$-Gladkii analiz i funktsionalno-differentsialnye uravneniya, IMM UrO RAN, Ekaterinburg, 1996
A. B. Kim, V. G. Pimenov, $i$-Gladkii analiz i chislennye metody resheniya funktsionalno-differentsialnykh uravnenii, Regulyarnaya i khaoticheskaya dinamika, M.–Izhevsk, 2004
A. B. Kim, Pryamoi metod Lyapunova v teorii ustoichivosti sistem s posledeistviem, Uralskii gosuniversitet, Ekaterinburg, 1992