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This article is cited in 13 scientific papers (total in 13 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
 Full text:
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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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Linking options:
http://mi.mathnet.ru/eng/mz8725https://doi.org/10.4213/mzm8725 http://mi.mathnet.ru/eng/mz/v90/i2/p280
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:
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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
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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
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D. K. Potapov, “On solutions of the Gol'dshtik problem”, Num. Anal. Appl., 5:4 (2012), 342–347
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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
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Potapov D.K. Yevstafyeva V.V., “Lavrent'Ev Problem for Separated Flows with an External Perturbation”, Electron. J. Differ. Equ., 2013, 255
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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
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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
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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
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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
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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
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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
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V. N. Pavlenko, D. K. Potapov, “Elenbaas Problem of Electric Arc Discharge”, Math. Notes, 103:1 (2018), 89–95
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V. N. Pavlenko, D. K. Potapov, “Properties of the spectrum of an elliptic boundary value problem with a parameter and a discontinuous nonlinearity”, Sb. Math., 210:7 (2019), 1043–1066
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