Averaging method and it's applications.
Generalization of Ljapunov's second method.
Сomputational methods in micromagnetic problems.
Variational method in optimal control problems.
Main publications:
Khapaev M.M., Usrednenie v teorii ustoichivosti: Issledovanie rezonansnykh mnogochastotnykh sistem, Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 1986
Khapaev M.M., “Stability investigation in 3-body problem based on hydrodynamic model of planets”, Doklady Akademii Nauk, 231:5 (1976), 1092–1095
Khapaev M.M., Osipov S.G., Ternovskii V.V., “Modelirovanie trekhmernykh periodicheskikh struktur v ferromagnitnykh plenkakh”, Doklady Akademii Nauk, 305:4 (1989), 831–834
Ternovskii V.V., Khapaev M.M., “Direct numerical method for solving optimal control problems”, Doklady Mathematics, 420:40 (2008), 463–466