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  AM&CP  » Structure » Staff » Potapov D. K.

Potapov Dmitriy Konstantinovich

[photo]

Ph.D., Associate Professor of Department of Higher Mathematics

Room 249, tel. (812) 428-42-44
E-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

  1. 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.
  2. 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.
  3. 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.
  4. D.K. Potapov, Spectral problems for equations with discontinuous monotone operators, J. Math. Sci., 144:(2007), no. 4, pp. 4232-4233.
  5. 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.
  6. 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.
  7. D.K. Potapov, Continuous approximations of Gol'dshtik’s model, Math. Notes, 87:(2010), no. 2, pp. 244-247.
  8. 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.
  9. D.K. Potapov, Bifurcation problems for equations of elliptic type with discontinuous nonlinearities, Math. Notes, 90:(2011), no. 2, pp. 260-264.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. D.K. Potapov, On solutions to the Goldshtik problem, Num. Anal. and Appl., 5:(2012), no. 4, pp. 342-347.
  16. D.K. Potapov, Spectral problems for variational inequalities with discontinuous operators, Math. Notes, 93:(2013), no. 2, pp. 288-296.
  17. 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.
  18. 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.
  19. 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.
  20. D.K. Potapov, On one problem of electrophysics with discontinuous nonlinearity, Differ. Equ., 50:(2014), no. 3, pp. 419-422.
  21. D.K. Potapov, Sturm-Liouville’s problem with discontinuous nonlinearity, Differ. Equ., 50:(2014), no. 9, pp. 1272-1274.
  22. 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.
  23. 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.
  24. 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.
  25. A.M. Kamachkin, D.K. Potapov, V.V. Yevstafyeva, 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. A.M. Kamachkin, D.K. Potapov, V.V. Yevstafyeva, 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.
  33. 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.
  34. 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.

Scientific publications

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Potapov D.K. Solutions of second-order differential equations with discontinuous right parts. Cambridge Scientific Publishers, 2016. P. 135-144.
  7. 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.
  8. 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.
  9. Potapov D.K. Spectral problems for equations with discontinuous monotone operators // Journal of Mathematical Sciences. 2007. Vol. 144. № 4. 4232-4233.