# Potapov Dmitriy Konstantinovich

Ph.D., Associate Professor of Department of Higher Mathematics Room 249, tel. (812) 428-42-44E-mail: d.potapov@spbu.ru |

## Academic degree and appointments

- 2003 Ph.D. in Mathematics, thesis "Eigenvalue Problems for Elliptic Equations with Discontinuous Nonlinearities", Ural State University
- 2001 M.Sc. in Mathematics (Diploma with Honours, 5.0 from 5.0), thesis "An Eigenvalue Set Structure for Equations with Discontinuous Nonlinearities", Faculty of Mathematics, Chelyabinsk State University

- since 2003 Associate Professor, Department of Higher Mathematics, Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University
- 2001-2003 Assistant, Department of Computing Mathematics, Faculty of Mathematics, Chelyabinsk State University

## Teaching responsibilities

- Mathematical Analysis
- Multiple Integrals and Series
- Non-Classical Logics

## Areas of research

- Nonlinear Functional Analysis
- Differential Equations with Discontinuous Nonlinearities
- Eigenvalue Problems
- Mathematical Modelling

## Publications

*V.N. Pavlenko, D.K. Potapov*, Existence of a ray of eigenvalues for equations with discontinuous operators, Siberian Math. J., 42:(2001), no. 4, pp. 766-773.*V.N. Pavlenko, D.K. Potapov,*Approximation of boundary value problems of elliptic type with a spectral parameter and discontinuous nonlinearity, Russ. Math. (Iz. VUZ), 49:(2005), no. 4, pp. 46-52.*D.K. Potapov*, Approximation to the Dirichlet problem for a higher-order elliptic equation with a spectral parameter and a discontinuous nonlinearity, Differ. Equ., 43:(2007), no. 7, pp. 1031-1032.*D.K. Potapov,*Spectral problems for equations with discontinuous monotone operators, J. Math. Sci., 144:(2007), no. 4, pp. 4232-4233.*D.K. Potapov*, On an upper bound for the value of the bifurcation parameter in eigenvalue problems for elliptic equations with discontinuous nonlinearities, Differ. Equ., 44:(2008), no. 5, pp. 737-739.*D.K. Potapov,*On the eigenvalue set structure for higher-order equations of elliptic type with discontinuous nonlinearities, Differ. Equ., 46:(2010), no. 1, pp. 155-157.*D.K. Potapov*, Continuous approximations of Gol'dshtik’s model, Math. Notes, 87:(2010), no. 2, pp. 244-247.*D.K. Potapov*, On a “separating” set for higher-order equations of elliptic type with discontinuous nonlinearities, Differ. Equ., 46:(2010), no. 3, pp. 458-460.*D.K. Potapov*, Bifurcation problems for equations of elliptic type with discontinuous nonlinearities, Math. Notes, 90:(2011), no. 2, pp. 260-264.*D.K. Potapov*, Continuous approximation for a 1D analog of the Gol'dshtik model for separated flows of an incompressible fluid, Num. Anal. and Appl., 4:(2011), no. 3, pp. 234-238.*D.K. Potapov,*Approximation of the one-parameter family of Dirichlet problems for higher-order elliptic-type equations with discontinuous nonlinearities in the resonance case, Math. Notes, 90:(2011), no. 3, pp. 451-454.*D.K. Potapov*, Estimation of the bifurcation parameter in spectral problems for equations with discontinuous operators, Ufa Math. J., 3:(2011), no. 1, pp. 42-44.*D.K. Potapov*, On a class of elliptic variational inequalities with a spectral parameter and discontinuous nonlinearity, Siberian Math. J., 53:(2012), no. 1, pp. 168-173.*D.K. Potapov*, On the number of semiregular solutions in problems with spectral parameter for higher-order equations of elliptic type with discontinuous nonlinearities, Differ. Equ., 48:(2012), no. 3, pp. 455-457.*D.K. Potapov*, On solutions to the Goldshtik problem, Num. Anal. and Appl., 5:(2012), no. 4, pp. 342-347.*D.K. Potapov*, Spectral problems for variational inequalities with discontinuous operators, Math. Notes, 93:(2013), no. 2, pp. 288-296.*D.K. Potapov*, Optimal control of higher order elliptic distributed systems with a spectral parameter and discontinuous nonlinearity, J. Comput. Syst. Sci. Int., 52:(2013), no. 2, pp. 180-185.*D.K. Potapov*, On a number of solutions in problems with spectral parameter for equations with discontinuous operators, Ufa Math. J., 5:(2013), no. 2, pp. 56-62.*D.K. Potapov, V.V. Yevstafyeva,*Lavrent’ev problem for separated flows with an external perturbation, Electron. J. Differ. Equ., (2013), no. 255, pp. 1-6.*D.K. Potapov*, On one problem of electrophysics with discontinuous nonlinearity, Differ. Equ., 50:(2014), no. 3, pp. 419-422.*D.K. Potapov*, Sturm-Liouville’s problem with discontinuous nonlinearity, Differ. Equ., 50:(2014), no. 9, pp. 1272-1274.*A.M. Kamachkin, D.K. Potapov, V.V. Yevstafyeva,*Solution to second-order differential equations with discontinuous right-hand side, Electron. J. Differ. Equ., (2014), no. 221, pp. 1-6.*D.K. Potapov*, Existence of solutions, estimates for the differential operator, and a "separating" set in a boundary value problem for a second-order differential equation with a discontinuous nonlinearity, Differ. Equ., 51:(2015), no. 7, pp. 967-972.*V.N. Pavlenko, D.K. Potapov*, The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities, Sbornik: Mathematics, 206:(2015), no. 9, pp. 1281-1298.Non-existence of periodic solutions to non-autonomous second-order differential equation with discontinuous nonlinearity, Electron. J. Differ. Equ., (2016), no. 04, pp. 1-8.*A.M. Kamachkin, D.K. Potapov, V.V. Yevstafyeva*,Existence of solutions for second-order differential equations with discontinuous right-hand side, Electron. J. Differ. Equ., (2016), no. 124, pp. 1-9.*A.M. Kamachkin, D.K. Potapov, V.V. Yevstafyeva*,*D.K.**Potapov,*Solutions of second-order differential equations with discontinuous right parts, Analytic Methods of Analysis and Differential Equations: AMADE 2015, Cambridge Scientific Publishers, (2016), pp. 135-144.*V.N. Pavlenko, D.K. Potapov*, Existence of solutions to a nonvariational elliptic boundary value problem with parameter and discontinuous nonlinearity, Siberian Adv. Math., 27:(2017), no. 1, pp. 16-25.*V.N. Pavlenko, D.K. Potapov*, Existence of two nontrivial solutions for sufficiently large values of the spectral parameter in eigenvalue problems for equations with discontinuous right-hand sides, Sbornik: Mathematics, 208:(2017), no. 1, pp. 157-172.*V.N. Pavlenko, D.K. Potapov*, Existence of three nontrivial solutions of an elliptic boundary-value problem with discontinuous nonlinearity in the case of strong resonance, Math. Notes, 101:(2017), no. 2, pp. 284-296.*V.N. Pavlenko, D.K. Potapov*, Estimates for a spectral parameter in elliptic boundary value problems with discontinuous nonlinearities, Siberian Math. J., 58:(2017), no. 2, pp. 288-295.Existence of periodic solutions to automatic control system with relay nonlinearity and sinusoidal external influence, Int. J. Robust Nonlinear Control, 27:(2017), no. 2, pp. 204-211.*A.M. Kamachkin, D.K. Potapov, V.V. Yevstafyeva*,Existence of subharmonic solutions to a hysteresis system with sinusoidal external influence, Electron. J. Differ. Equ., (2017), no. 140, pp. 1-10.*A.M. Kamachkin, D.K. Potapov, V.V. Yevstafyeva*,, On uniqueness and properties of periodic solution of second-order nonautonomous system with discontinuous nonlinearity, J. Dyn. Control Syst., 23:(2017), no. 4, pp. 825-837.*A.M. Kamachkin, D.K. Potapov, V.V. Yevstafyeva*

## Scientific publications

- Kamachkin A.M., Potapov D.K., Yevstafyeva V.V. Existence of periodic solutions to automatic control system with relay nonlinearity and sinusoidal external influence // International Journal of Robust and Nonlinear Control. 2017. Vol. 27. № 2. P. 204-211.
- Kamachkin A.M., Potapov D.K., Yevstafyeva V.V. Existence of subharmonic solutions to a hysteresis system with sinusoidal external influence // Electronic Journal of Differential Equations. 2017. № 140. P. 1-10.
- Kamachkin A.M., Potapov D.K., Yevstafyeva V.V. On uniqueness and properties of periodic solution of second-order nonautonomous system with discontinuous nonlinearity // Journal of Dynamical and Control Systems. 2017. Vol. 23. № 4. P. 825-837.
- Kamachkin A.M., Potapov D.K., Yevstafyeva V.V. Existence of solutions for second-order differential equations with discontinuous right-hand side // Electronic Journal of Differential Equations. 2016. № 124. P. 1-9.
- Kamachkin A.M., Potapov D.K., Yevstafyeva V.V. Non-existence of periodic solutions to non-autonomous second-order differential equation with discontinuous nonlinearity // Electronic Journal of Differential Equations. 2016. № 04. P. 1-8.
- Potapov D.K. Solutions of second-order differential equations with discontinuous right parts. Cambridge Scientific Publishers, 2016. P. 135-144.
- Kamachkin A.M., Potapov D.K., Yevstafyeva V.V. Solution to second-order differential equations with discontinuous right-hand side // Electronic Journal of Differential Equations. 2014. № 221. P. 1-6.
- Potapov D.K., Yevstafyeva V.V. Lavrent'ev problem for separated flows with an external perturbation // Electronic Journal of Differential Equations. 2013. № 255. P. 1–6.
- Potapov D.K. Spectral problems for equations with discontinuous monotone operators // Journal of Mathematical Sciences. 2007. Vol. 144. № 4. 4232-4233.