Area of scientific concerns is the theory of function differential equations. Ph.D. thesis is dedicated by functional differential equations with Volterra operators. I have the publications by the stability of differential equations with delaying argument and by the theory of a reducibility of function differential equations. Last activities are dedicated to generalized variational problems, in particular, variational problems with deviating argument.
Main publications:
Gusarenko S. A. Ob odnom obobschenii ponyatiya volterrova operatora // Doklady AN SSSR, 1987, 295(5), 1046–1049.
Gusarenko S. A., Domoshnitskii A. I. Ob asimptoticheskikh i ostsillyatsionnykh svoistvakh lineinykh skalyarnykh funktsionalno-differentsialnykh uravnenii pervogo poryadka // Differents. uravneniya, 1989, 25(12), 2090–2103.
Gusarenko S. A. Kriterii privodimosti operatornykh uravnenii // Izv. vuzov. Matematika, 1993, 5, 43–45.
Gusarenko S. A. O variatsionnykh zadachakh s lineinymi ogranicheniyami // Izv. vuzov. Matematika, 1999, 2, 41–55.
Azbelev N. V., Bravyi E. I., Gusarenko S. A. K voprosu ob effektivnykh dostatochnykh usloviyakh razreshimosti variatsionnykh zadach // Doklady RAN, 2001, 381(2), 1–4.
