Geodesic
On the solution of Hammerstein integral equations with loads and bifurcation parameters
The Bulletin of Irkutsk State University. Series Mathematics, Tome 43 (2023), pp. 78-90 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The Hammerstein integral equation with loads on the desired solution is considered. The equation contains a parameter for any value of which the equation has a trivial solution. Necessary and sufficient conditions are obtained for the coefficients of the equation and those values of the parameter (bifurcation points) in its neighborhood the equation has a nontrivial real solutions. The leading terms of the asymptotics of such branches of solutions are constructed. Examples are given illustrating the proven existence theorems.
Keywords: Hammerstein equation, branching, asymptotics, loads.
Mots-clés : bifurcation points 
@article{IIGUM_2023_43_a5,
     author = {N. A. Sidorov and Lev Ryan D. Dreglea Sidorov},
     title = {On the solution of {Hammerstein} integral equations with loads and bifurcation parameters},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {78--90},
     year = {2023},
     volume = {43},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2023_43_a5/}
}
TY  - JOUR
AU  - N. A. Sidorov
AU  - Lev Ryan D. Dreglea Sidorov
TI  - On the solution of Hammerstein integral equations with loads and bifurcation parameters
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2023
SP  - 78
EP  - 90
VL  - 43
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2023_43_a5/
LA  - ru
ID  - IIGUM_2023_43_a5
ER  - 
%0 Journal Article
%A N. A. Sidorov
%A Lev Ryan D. Dreglea Sidorov
%T On the solution of Hammerstein integral equations with loads and bifurcation parameters
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2023
%P 78-90
%V 43
%U http://geodesic.mathdoc.fr/item/IIGUM_2023_43_a5/
%G ru
%F IIGUM_2023_43_a5
N. A. Sidorov; Lev Ryan D. Dreglea Sidorov. On the solution of Hammerstein integral equations with loads and bifurcation parameters. The Bulletin of Irkutsk State University. Series Mathematics, Tome 43 (2023), pp. 78-90. http://geodesic.mathdoc.fr/item/IIGUM_2023_43_a5/

[1] Bruno A. D., Power Geometry in Algebraic and Differential Equations, Elsevier, Amsterdam, 2000

[2] Vainberg M. M., Trenogin V. A., Theory of branching of solutions of nonlinear equations, Wolters-Noordhoff B.V, Groningen, 1964, 510 pp.

[3] Volkov V. T., Yagola A. G., Integral equations. Calculus of Variations, Course of lectures: textbook, KDU, M., 2008 (in Russian)

[4] Krasnov M. L., Kiselev A. I., Makarenko G. I., Integral equations: tasks and examples with solutions, Editorial URSS Publ, M., 2003 (in Russian)

[5] Nahushev A. M., Loaded equations and their applications, Nauka Publ, M., 2012 (in Russian)

[6] Romanova O. A., Sidorov N. A., “On the construction of the trajectory of a dynamical system with initial data on the hyperplanes”, The Bulletin of Irkutsk State University. Series Mathematics, 12 (2015), 93–105

[7] Sidorov N. A., Dreglea Sidorov L. R. D., “On Bifurcation Points of the Solution of the Hammerstein Integral Equation with Loads”, Dynamical Systems and Computer Science: Theory and Applications, DYSC 2022, Proceedings of the 4th International Conference (Irkutsk, September 19–22, 2022), 2022, 41–44 (in Russian)

[8] Sidorov N. A., Leont'ev R.Ju., “On solutions of the maximum order of smallness of nonlinear equations with a vector parameter in sectoral neighborhoods”, Tr. IMM UrO RAN, 16, no. 2, 2010, 226–237 (in Russian)

[9] Sidorov N. A., Sidorov D. N., “Nonlinear Volterra Equations with Loads and Bifurcation Parameters: Existence Theorems and Construction of Solutions”, Differantial Equations, 57 (2021), 1640–1651 | DOI | DOI

[10] Sidorov N. A., Sidorov L. D., “On the role of the spectrum of one class of integral-functional operators in solving nonlinear Volterra equations with loads”, Proceedings of the 7th International Conference on Nonlinear Analysis and Extremal Problems, NLA-2022, Irkutsk, 2022, 115–116

[11] Trénoguine V. A., Analyse fonctionnelle, traduit du russe par V. Kotliar, Éd. Mir, 1985

[12] Sidorov N. A., “Special Issue Editorial Solvability of Nonlinear Equations with Parameters: Branching, Regularization, Group Symmetry and Solutions Blow-Up”, Symmetry, 14:2 (2022), 226, 4 pp. | DOI

[13] Sidorov N. A., Sidorov D. N., Sinitsyn A. V., “Toward general theory of differential-operator and kinetic models”, World Scientific Series on Nonlinear Science Series A, 97, ed. L. Chua, World Scientific, S'pore, 2020, 496 pp. | DOI

[14] Sidorov N., Loginov B., Sinitsyn A., Falaleev M., Lyapunov-Schmidt methods in nonlinear analysis and applications, Mathematics and its Application Ser., 550, Kluwer Publ, Dordrecht, 2002 | DOI