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Mat. Zametki, 2011, Volume 90, Issue 2, Pages 280–284 (Mi mz8725)  

This article is cited in 12 scientific papers (total in 12 papers)

Bifurcation Problems for Equations of Elliptic Type with Discontinuous Nonlinearities

D. K. Potapov

Saint-Petersburg State University

Abstract: We consider the problem of the existence of semiregular solutions to the main boundary-value problems for second-order equations of elliptic type with a spectral parameter and discontinuous nonlinearities. A variational method is used to obtain the theorem on the existence of solutions and properties of the “separating” set for the problems under consideration. The results obtained are applied to the Goldshtik problem.

Keywords: second-order equation of elliptic type, bifurcation problem, semiregular solution, Carathéodory function, Dirichlet boundary condition, Neumann boundary condition

DOI: https://doi.org/10.4213/mzm8725

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English version:
Mathematical Notes, 2011, 90:2, 260–264

Bibliographic databases:

UDC: 517.95
Received: 15.03.2010

Citation: D. K. Potapov, “Bifurcation Problems for Equations of Elliptic Type with Discontinuous Nonlinearities”, Mat. Zametki, 90:2 (2011), 280–284; Math. Notes, 90:2 (2011), 260–264

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dmitrii K. Potapov, “Zadachi upravleniya dlya uravnenii so spektralnym parametrom i razryvnym operatorom pri nalichii vozmuschenii”, Zhurn. SFU. Ser. Matem. i fiz., 5:2 (2012), 239–245  mathnet
    2. D. K. Potapov, “O kharaktere razryvov nelineinosti v zadachakh na sobstvennye znacheniya dlya uravnenii ellipticheskogo tipa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 3(28) (2012), 188–190  mathnet  crossref  zmath
    3. D. K. Potapov, “On solutions of the Gol'dshtik problem”, Num. Anal. Appl., 5:4 (2012), 342–347  mathnet  crossref  elib
    4. A. V. Vasin, “Opredelenie linii razdela oblastei vikhrevykh techenii”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 2013, no. 1, 3–10  mathnet
    5. Potapov D.K. Yevstafyeva V.V., “Lavrent'Ev Problem for Separated Flows with an External Perturbation”, Electron. J. Differ. Equ., 2013, 255  mathscinet  zmath  isi
    6. Kamachkin A.M., Potapov D.K., Yevstafyeva V.V., “Solution To Second-Order Differential Equations With Discontinuous Right-Hand Side”, Electron. J. Differ. Equ., 2014, 221  mathscinet  zmath  isi
    7. Potapov D.K., “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., 51:7 (2015), 967–972  crossref  mathscinet  zmath  isi  elib  scopus
    8. V. N. Pavlenko, D. K. Potapov, “Existence of solutions to a nonvariational elliptic boundary value problem with parameter and discontinuous nonlinearity”, Siberian Adv. Math., 27:1 (2017), 16–25  mathnet  crossref  crossref  mathscinet  elib
    9. Kamachkin A.M., Potapov D.K., Yevstafyeva V.V., “Existence of Solutions For Second-Order Differential Equations With Discontinuous Right-Hand Side”, Electron. J. Differ. Equ., 2016  mathscinet  isi
    10. 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, 101:2 (2017), 284–296  mathnet  crossref  crossref  mathscinet  isi  elib
    11. V. N. Pavlenko, D. K. Potapov, “Estimates for a spectral parameter in elliptic boundary value problems with discontinuous nonlinearities”, Siberian Math. J., 58:2 (2017), 288–295  mathnet  crossref  crossref  isi  elib  elib
    12. V. N. Pavlenko, D. K. Potapov, “Elenbaas Problem of Electric Arc Discharge”, Math. Notes, 103:1 (2018), 89–95  mathnet  crossref  crossref  isi  elib
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