Abstract:
The method of weighted metrics in the cone of the space of continuous functions is used to prove a global theorem on the existence and uniqueness of a nonnegative nontrivial solution for a system of integro-differential equations of convolution type with power nonlinearity. It is shown that the solution can be found by the method of successive approximations of the Picard type and exact a priori estimates are obtained for it.
Keywords:
system of integro-differential equations, convolution, power nonlinearity.
Citation:
S. N. Askhabov, “System of integro-differential equations of convolution type with power nonlinearity”, Sib. Zh. Ind. Mat., 24:3 (2021), 5–18
\Bibitem{Ask21}
\by S.~N.~Askhabov
\paper System of integro-differential equations of convolution type with power nonlinearity
\jour Sib. Zh. Ind. Mat.
\yr 2021
\vol 24
\issue 3
\pages 5--18
\mathnet{http://mi.mathnet.ru/sjim1138}
\crossref{https://doi.org/10.33048/SIBJIM.2021.24.301}
Linking options:
https://www.mathnet.ru/eng/sjim1138
https://www.mathnet.ru/eng/sjim/v24/i3/p5
This publication is cited in the following 2 articles:
S. N. Askhabov, “Integral Equation with the Toeplitz–Hankel Kernel and an Inhomogeneity in the Linear Part”, Vestnik St.Petersb. Univ.Math., 57:4 (2024), 462
S. N. Askhabov, “Nachalnaya zadacha dlya integro-differentsialnogo uravneniya s raznostnymi yadrami i neodnorodnostyu v lineinoi chasti”, Differentsialnye uravneniya i matematicheskaya fizika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 225, VINITI RAN, M., 2023, 3–13
Citation in format AMSBIB
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