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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, Issue 1(26), Pages 251–255 (Mi vsgtu1045)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communication
Differential Equations

On number of solutions in eigenvalue problems for elliptic equations with discontinuous nonlinearities

D. K. Potapov

St. Petersburg State University, St. Petersburg, Russia

Abstract: We study the existence of solutions of eigenvalue problems for elliptic equations of the second order with nonlinearity discontinuous with respect to a phase variable. Using the variational method, we receive the theorems on number of solutions for investigated problems. M. A. Gol'dshtik's problem on separated flows of incompressible fluid is considered as an appendix.

Keywords: boundary value problems, elliptic equations, eigenvalue problems, discontinuous nonlinearity, variational method, number of solutions

DOI: https://doi.org/10.14498/vsgtu1045

Full text: PDF file (398 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.956.2
MSC: Primary 35J25; Secondary 35P30, 35J60, 35P15
Original article submitted 29/XI/2011
revision submitted – 17/II/2012

Citation: D. K. Potapov, “On number of solutions in eigenvalue problems for elliptic equations with discontinuous nonlinearities”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(26) (2012), 251–255

Citation in format AMSBIB
\Bibitem{Pot12}
\by D.~K.~Potapov
\paper On number of solutions in eigenvalue problems for elliptic equations with discontinuous nonlinearities
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 1(26)
\pages 251--255
\mathnet{http://mi.mathnet.ru/vsgtu1045}
\crossref{https://doi.org/10.14498/vsgtu1045}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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