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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)
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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
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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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http://mi.mathnet.ru/eng/vsgtu1045 http://mi.mathnet.ru/eng/vsgtu/v126/p251
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This publication is cited in the following articles:
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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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