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Mat. Sb. (N.S.), 1978, Volume 107(149), Number 2(10), Pages 218–226 (Mi msb2645)  

This article is cited in 2 scientific papers (total in 2 papers)

On the theory of upper and lower solutions and the solvability of quasilinear integro-differential equations

V. P. Polityukov


Abstract: In this paper nonlinear integro-differential equations of the type $\partial u/\partial t-\Delta u=\Phi(x,t,u,F(u))$ are considered, where $F(u)$ is a nonlinear integral operator.
The concepts of upper and lower solutions of problems for nonlinear integro-differential equations are defined, and based on this new solvability criteria for these problems are obtained. Nonstationary, as well as stationary, integro-differential equations are considered.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:4, 499–507

Bibliographic databases:

UDC: 517.948.34
MSC: 45K05
Received: 18.11.1977

Citation: V. P. Polityukov, “On the theory of upper and lower solutions and the solvability of quasilinear integro-differential equations”, Mat. Sb. (N.S.), 107(149):2(10) (1978), 218–226; Math. USSR-Sb., 35:4 (1979), 499–507

Citation in format AMSBIB
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\by V.~P.~Polityukov
\paper On the theory of upper and lower solutions and the solvability of quasilinear integro-differential equations
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 107(149)
\issue 2(10)
\pages 218--226
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=512008}
\zmath{https://zbmath.org/?q=an:0431.45010|0413.45007}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 4
\pages 499--507
\crossref{https://doi.org/10.1070/SM1979v035n04ABEH001568}
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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. J. Bebernes, R. Ely, “Existence and invariance for parabolic functional equations”, Nonlinear Analysis: Theory, Methods & Applications, 7:11 (1983), 1225  crossref
    2. Reinhard Redlinger, “Existence theorems for semilinear parabolic systems with functionals”, Nonlinear Analysis: Theory, Methods & Applications, 8:6 (1984), 667  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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