Geodesic
System of integro-differential equations of convolution type with power nonlinearity
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 3, pp. 5-18.

Voir la notice de l'article provenant de la source Math-Net.Ru

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, power nonlinearity.
Mots-clés : convolution 
@article{SJIM_2021_24_3_a0,
     author = {S. N. Askhabov},
     title = {System of integro-differential equations of convolution type with power nonlinearity},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {5--18},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2021_24_3_a0/}
}
TY  - JOUR
AU  - S. N. Askhabov
TI  - System of integro-differential equations of convolution type with power nonlinearity
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2021
SP  - 5
EP  - 18
VL  - 24
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2021_24_3_a0/
LA  - ru
ID  - SJIM_2021_24_3_a0
ER  - 
%0 Journal Article
%A S. N. Askhabov
%T System of integro-differential equations of convolution type with power nonlinearity
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2021
%P 5-18
%V 24
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2021_24_3_a0/
%G ru
%F SJIM_2021_24_3_a0
S. N. Askhabov. System of integro-differential equations of convolution type with power nonlinearity. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 3, pp. 5-18. http://geodesic.mathdoc.fr/item/SJIM_2021_24_3_a0/

[1] S. N. Askhabov, N. K. Karapetyants, A. Ya. Yakubov, “Integral equations of convolution type with power nonlinearity and systems of such equations”, Dokl. Math., 41:2 (1990), 323–327 | Zbl

[2] S. N. Askhabov, M. A. Betilgiriev, “Nonlinear integral equations of convolution type with almost increasing kernels in cones”, Differ. Equat., 27:2 (1991), 234–242 | Zbl

[3] S. N. Askhabov, Nonlinear Convolution Type Equations, Fizmatlit, M., 2009 (in Russian)

[4] W. Okrasinski, “On the existence and uniqueness of non-negative solutions of a certain non-linear convolution equation”, Ann. Polon. Math., 36:1 (1976), 61–72 | DOI

[5] W. Okrasinski, “Nonlinear Volterra equations and physical applications”, Extracta Math., 4:2 (1989), 51–74

[6] J. J. Keller, “Propagation of simple nonlinear waves in gas filled tubes with friction”, Z. Angew. Math. Phys., 32:2 (1981), 170–181 | DOI | Zbl

[7] A. N. Tikhonov, “On the cooling of bodies during radiation, following the Stefan-Boltzmann law”, Izv. AN USSR, Department of Mathematics and Natural Sciences, Series of Geogr. And Geophysics, 3 (1937), 461–479 (in Russian)

[8] G. B. Ermentrout, J. D. Cowan, “Secondary bifurcation in neuronal nets”, SIAM J. Appl. Math., 39:2 (1980), 323–340 | DOI | Zbl

[9] L. v. Wolfersdorf, “Eininge klassen quadratischer integralgleichungen”, Sitz. Sachs. Akad. Wiss. Leipzig. Math. naturwiss. Klasse, 128:2 (2000), 1–34

[10] H. Brunner, Volterra Integral Equations: an Introduction to the Theory and Applications, Univ. Press, Cambridge, 2017

[11] R. Edvards, Functional Analysis: Theory and Applications, Holt, Rinehart, and Winston, N.Y., 1965

[12] S. N. Askhabov, “Integro-differential equation of the convolution type with a power nonlinearity and an inhomogeneity in the linear part”, Differ. Equat., 56:6 (2020), 775–784 | DOI | Zbl

[13] S. N. Askhabov, N. K. Karapetyants, “Discrete equations of convolution type with monotone nonlinearity”, Differ. Equat., 25:10 (1989), 1255–1261 | Zbl

[14] S. N. Askhabov, N. K. Karapetian, “Convolution type discrete equations with monotonous nonlinearity in comples spaces”, J. Integral Equat. Math. Phys., 1:1 (1992), 44–66

[15] S. N. Askhabov, N. K. Karapetyants, “Discrete equations of convolution type with monotone nonlinearity in complex spaces”, Dokl. Math., 45:1 (1992), 206–210 | Zbl