Nonlinear operator equations with functionaly modified argument
The Bulletin of Irkutsk State University. Series Mathematics, Tome 3 (2010) no. 4, pp. 96-113 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Local solution of equation with functionaly modified argument is found. Method of Neuton’s diagramm is used to consider the nonlinear operator equation with functionaly modified argument. The local solution is built in a class of continious function with logariphmic asymptoty.
Keywords: functionaly modified argument, nonlinear operator equation.
@article{IIGUM_2010_3_4_a10,
     author = {N. A. Sidorov and A. V. Trufanov},
     title = {Nonlinear operator equations with functionaly modified argument},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {96--113},
     year = {2010},
     volume = {3},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2010_3_4_a10/}
}
TY  - JOUR
AU  - N. A. Sidorov
AU  - A. V. Trufanov
TI  - Nonlinear operator equations with functionaly modified argument
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2010
SP  - 96
EP  - 113
VL  - 3
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2010_3_4_a10/
LA  - ru
ID  - IIGUM_2010_3_4_a10
ER  - 
%0 Journal Article
%A N. A. Sidorov
%A A. V. Trufanov
%T Nonlinear operator equations with functionaly modified argument
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2010
%P 96-113
%V 3
%N 4
%U http://geodesic.mathdoc.fr/item/IIGUM_2010_3_4_a10/
%G ru
%F IIGUM_2010_3_4_a10
N. A. Sidorov; A. V. Trufanov. Nonlinear operator equations with functionaly modified argument. The Bulletin of Irkutsk State University. Series Mathematics, Tome 3 (2010) no. 4, pp. 96-113. http://geodesic.mathdoc.fr/item/IIGUM_2010_3_4_a10/

[1] M. M. Vainberg, V. A. Trenogin, Teoriya vetvleniya reshenii nelineinykh uravnenii, Nauka, M., 1969, 527 pp. | MR

[2] B. V. Loginov, Teoriya vetvleniya reshenii nelineinykh uravnenii v usloviyakh gruppovoi simmetrii, Fan, Tashkent, 1985, 184 pp. | MR | Zbl

[3] N. A. Sidorov, D. N. Sidorov, A. V. Trufanov, “Postroenie obobschennykh reshenii nelineinykh integro-differentsialnykh uravnenii”, Vestn. MAGU. Matematika, 2005, no. 8, 123–138

[4] N. A. Sidorov, A. V. Trufanov, “Struktura reshenii lineinykh operatornykh uravnenii c funktsionalnym vozmuscheniem argumenta”, Tr. Srednevolzh. Mat. o-va, 1:8 (2006), 104–109 | Zbl

[5] N. A. Sidorov, Obschie voprosy regulyarizatsii v zadachakh teorii vetvleniya, Gl. 4, Izd-vo IGU, Irkutsk, 1982 | MR | Zbl

[6] N. A. Sidorov, A. V. Trufanov, “Nelineinye operatornye uravneniya s funktsionalnym vozmuscheniem argumenta neitralnogo tipa”, Differents. uravneniya, 45:12 (2009), 1804–1808 | MR | Zbl

[7] V. A. Trenogin, Funktsionalnyi analiz, Fizmatlit, M., 2002, 488 pp.

[8] A. V. Trufanov, “Kvazilineinye operatornye uravneniya s funktsionalnymi vozmuscheniyami neitralnogo tipa”, Vestn. Samar. gos. tekhn. un-ta, 2007, no. 2 (6), 104–109 | Zbl

[9] A. V. Trufanov, “Nelineinye operatornye uravneniya s funktsionalnym vozmuscheniem argumenta”, Izv. Irkut. gos. un-ta. Ser.: Matematika, 2007, no. 1, 308–321

[10] A. V. Trufanov, O. V. Brovko, “Lineinye operatornye uravneniya dvukh peremennykh s funktsionalnymi vozmuscheniyami argumentov”, Trudy III mezhvuzovskoi zonalnoi konferentsii, posvyaschennoi pamyati prof. B. A. Beltyukova (Irkutsk, 2007), 72–74

[11] A. S. Apartsyn, Nonclassical Linear Volterra Equations of the First Kind, VSP Brill Academic Publishers, Zeist, 2003, 195 pp. | MR | Zbl

[12] K. Baron, R. Ger, J. Matkowski, “Analytic solutions of a system of functional equations”, Publs. math., 22:3–4 (1975), 189–194 | MR | Zbl

[13] A. M. Denisov, A. Lorenzi, “Existence results and regularisation techniques for severely iss-posed integro-functoinal equations”, Universita degli studi di Milano, quardno, 1996, no. 9, 14 | Zbl

[14] N. Sidorov et al., Lyapunov–Schmidt Methods in Nonlinear Analysis and Applications, Kluwer Academic Publishers, Dordrecht–Boston–London, 2002, 547 pp. | MR | Zbl

[15] N. A. Sidorov, D. N. Sidorov, A. V. Trufanov, “Generalized solutions of nonluinear integral-functional equations”, Nonlinear boundary problems, 16 (2006), 96–106 | MR | Zbl

[16] W. Smajdor, “Local analytic solutions of functional equations”, Annal Polon. math., 19:1 (1967), 37–45 | MR | Zbl

[17] W. Smajdor, “Local analytic solutions of functional equations”, Annal Polon. math., 24 (1970), 39–43 | MR | Zbl