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.
Citation:
V. P. Polityukov, “On the theory of upper and lower solutions and the solvability of quasilinear integro-differential equations”, Math. USSR-Sb., 35:4 (1979), 499–507
\Bibitem{Pol78}
\by V.~P.~Polityukov
\paper On the theory of upper and lower solutions and the solvability of quasilinear integro-differential equations
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 4
\pages 499--507
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Linking options:
https://www.mathnet.ru/eng/sm2645
https://doi.org/10.1070/SM1979v035n04ABEH001568
https://www.mathnet.ru/eng/sm/v149/i2/p218
This publication is cited in the following 2 articles:
Reinhard Redlinger, “Existence theorems for semilinear parabolic systems with functionals”, Nonlinear Analysis: Theory, Methods & Applications, 8:6 (1984), 667
J. Bebernes, R. Ely, “Existence and invariance for parabolic functional equations”, Nonlinear Analysis: Theory, Methods & Applications, 7:11 (1983), 1225
Citation in format AMSBIB
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