01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
22.04.1956
E-mail:
Keywords:
functional differential equations; boundary value problems; variational problems; extreme problems.
Subject:
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.
Biography
Graduated from Faculty of Mathematics and Mechanics of Perm State University (PSU) in 1978. Ph.D. thesis was defended in 1987. A list of my works contains more than 40 titles. A member of Perm Seminar of functional differential equations.
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.
S. A. Gusarenko, “Stability criterion for linear differential equations with a delayed argument”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 12, 34–56; Russian Math. (Iz. VUZ), 66:12 (2022), 33–52
2004
2.
N. V. Azbelev, E. I. Bravyi, S. A. Gusarenko, “On Effective Solvability Conditions for Variational Problems”, Differ. Uravn., 40:2 (2004), 147–153; Differ. Equ., 40:2 (2004), 151–158
2002
3.
S. A. Gusarenko, “On conditions for the positive-definiteness of operators in a Hilbert space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2002, no. 1, 17–20; Russian Math. (Iz. VUZ), 46:1 (2002), 15–18
2000
4.
S. A. Gusarenko, “On the minimization of quadratic functionals with equality constraints”, Izv. Vyssh. Uchebn. Zaved. Mat., 2000, no. 4, 66–69; Russian Math. (Iz. VUZ), 44:4 (2000), 64–67
1999
5.
S. A. Gusarenko, “On variational problems with linear constraints”, Izv. Vyssh. Uchebn. Zaved. Mat., 1999, no. 2, 30–44; Russian Math. (Iz. VUZ), 43:2 (1999), 27–41
A. A. Gruzdev, S. A. Gusarenko, “On the reduction of variational problems to extremal problems without constraints”, Izv. Vyssh. Uchebn. Zaved. Mat., 1994, no. 6, 39–49; Russian Math. (Iz. VUZ), 38:6 (1994), 37–47
S. A. Gusarenko, “A criterion for the reducibility of operator equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, no. 5, 43–45; Russian Math. (Iz. VUZ), 37:5 (1993), 37–39
1989
8.
S. A. Gusarenko, A. I. Domoshnitskii, “Asymptotic and oscillation properties of first-order linear scalar functional-differential equations”, Differ. Uravn., 25:12 (1989), 2090–2103; Differ. Equ., 25:12 (1989), 1480–1491
S. A. Gusarenko, “A generalization of the concept of a Volterra operator”, Dokl. Akad. Nauk SSSR, 295:5 (1987), 1046–1049; Dokl. Math., 36:1 (1988), 156–159
S. A. Gusarenko, E. S. Zhukovskiy, V. P. Maksimov, “On the theory of functional-differential equations with locally Volterra operators”, Dokl. Akad. Nauk SSSR, 287:2 (1986), 268–272
S. A. Gusarenko, “On extendability of solutions of functional-differential equations with delay depending on the unknown function”, Differ. Uravn., 21:12 (1985), 2171–2173
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