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Matematicheskie Trudy, 2016, Volume 19, Number 1, Pages 91–105
DOI: https://doi.org/10.17377/mattrudy.2016.19.104 (Mi mt301) 		 
This article is cited in 6 scientific papers (total in 7 papers)

Existence of solutions to a nonvariational elliptic boundary value problem with parameter and discontinuous nonlinearity

V. N. Pavlenkoa, D. K. Potapovb

a Chelyabinsk State University, Chelyabinsk, Russia
b Saint Petersburg State University, Saint Petersburg, Russia
Full-text PDF (219 kB) Citations (7)
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DOI: https://doi.org/10.17377/mattrudy.2016.19.104
Abstract: We consider the question of the existence of the Dirichlet problem for second-order elliptic equations with spectral parameter and a nonlinearity discontinuous with respect to the phase variable. Here it is not assumed that the differential operator is formally selfadjoint. Using the method of upper and lower solutions, we establish results on the existence of nontrivial (positive and negative) solutions under positive values of the spectral parameter for the problems under study.
Key words: nonselfadjoint differential operator, spectral parameter, discontinuous nonlinearity, method of upper and lower solutions, nontrivial solution.
Received: 01.09.2015
English version:
Siberian Advances in Mathematics, 2017, Volume 27, Issue 1, Pages 16–25
DOI: https://doi.org/10.3103/S1055134417010023
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
Citation: V. N. Pavlenko, D. K. Potapov, “Existence of solutions to a nonvariational elliptic boundary value problem with parameter and discontinuous nonlinearity”, Mat. Tr., 19:1 (2016), 91–105; Siberian Adv. Math., 27:1 (2017), 16–25
Citation in format AMSBIB
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\by V.~N.~Pavlenko, D.~K.~Potapov
\paper Existence of solutions to a nonvariational elliptic boundary value problem with parameter and discontinuous nonlinearity
\jour Mat. Tr.
\yr 2016
\vol 19
\issue 1
\pages 91--105
\mathnet{http://mi.mathnet.ru/mt301}
\crossref{https://doi.org/10.17377/mattrudy.2016.19.104}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3588300}
\elib{https://elibrary.ru/item.asp?id=25963586}
\transl
\jour Siberian Adv. Math.
\yr 2017
\vol 27
\issue 1
\pages 16--25
\crossref{https://doi.org/10.3103/S1055134417010023}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014007934}
Linking options:
  • https://www.mathnet.ru/eng/mt301
  • https://www.mathnet.ru/eng/mt/v19/i1/p91
    • This publication is cited in the following 7 articles:
    1. O. V. Baskov, D. K. Potapov, “Existence of Solutions to the Non-Self-Adjoint Sturm–Liouville Problem with Discontinuous Nonlinearity”, Comput. Math. and Math. Phys., 64:6 (2024), 1254  crossref
    2. V. N. Pavlenko, D. K. Potapov, “One class of quasilinear elliptic type equations with discontinuous nonlinearities”, Izv. Math., 86:6 (2022), 1162–1178  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. V. N. Pavlenko, D. K. Potapov, “Positive solutions of superlinear elliptic problems with discontinuous non-linearities”, Izv. Math., 85:2 (2021), 262–278  mathnet  crossref  crossref  zmath  adsnasa  isi  elib
    4. V. N. Pavlenko, D. K. Potapov, “On a class of elliptic boundary-value problems with parameter and discontinuous non-linearity”, Izv. Math., 84:3 (2020), 592–607  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. V. N. Pavlenko, D. K. Potapov, “On the Existence of Three Nontrivial Solutions of a Resonance Elliptic Boundary Value Problem with a Discontinuous Nonlinearity”, Diff Equat, 56:7 (2020), 831  crossref
    6. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. S. M. Voronin, S. F. Dolbeeva, O. N. Dementev, A. A. Ershov, M. G. Lepchinskii, S. V. Matveev, N. B. Medvedeva, D. K. Potapov, E. A. Rozhdestvenskaya, E. A. Sbrodova, I. M. Sokolinskaya, A. A. Solovev, V. I. Ukhobotov, V. E. Fedorov, “K 70-letiyu professora Vyacheslava Nikolaevicha Pavlenko”, Chelyab. fiz.-matem. zhurn., 2:4 (2017), 383–387  mathnet  elib
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические труды Siberian Advances in Mathematics
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