The asymptotic behavior of solutions of a certain nonlinear Volterra equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 35-44 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the asymptotic behavior of bounded and unbounded solutions to the Volterra–Hammerstein equation. We obtain conditions for the admissibility of pairs of spaces of functions representable as a sum of a quasipolynomial and a subsum of the Taylor expansion at the point in infinity.
Keywords: asymptotic behavior
Mots-clés : Volterra–Hammerstein equations.
@article{IVM_2012_7_a3,
     author = {Z. B. Tsalyuk and M. V. Tsalyuk},
     title = {The asymptotic behavior of solutions of a~certain nonlinear {Volterra} equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {35--44},
     year = {2012},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_7_a3/}
}
TY  - JOUR
AU  - Z. B. Tsalyuk
AU  - M. V. Tsalyuk
TI  - The asymptotic behavior of solutions of a certain nonlinear Volterra equation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2012
SP  - 35
EP  - 44
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/IVM_2012_7_a3/
LA  - ru
ID  - IVM_2012_7_a3
ER  - 
%0 Journal Article
%A Z. B. Tsalyuk
%A M. V. Tsalyuk
%T The asymptotic behavior of solutions of a certain nonlinear Volterra equation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2012
%P 35-44
%N 7
%U http://geodesic.mathdoc.fr/item/IVM_2012_7_a3/
%G ru
%F IVM_2012_7_a3
Z. B. Tsalyuk; M. V. Tsalyuk. The asymptotic behavior of solutions of a certain nonlinear Volterra equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 35-44. http://geodesic.mathdoc.fr/item/IVM_2012_7_a3/

[1] Derbenev V. A., Tsalyuk Z. B., Asimptotika reshenii lineinykh uravnenii Volterra s raznostnym yadrom, KubGU, Krasnodar, 2001

[2] Tsalyuk Z. B., “Asimptotika rezolventy uravneniya Volterra s raznostnym yadrom pri stepennykh osobennostyakh simvola”, Izv. vuzov. Matem., 2006, no. 7, 77–84 | MR

[3] Tsalyuk Z. B., Tsalyuk M. V., “Struktura rezolventy uravneniya Volterra s nesummiruemym raznostnym yadrom”, Izv. vuzov. Matem., 2010, no. 4, 72–82 | MR | Zbl

[4] Levin J. J., Shea D. E., “On the asymptotic behavior of the bounded solutions of some integral equations. I”, J. Math. Anal. Appl., 37:1 (1972), 42–82 | DOI | MR | Zbl

[5] Levin J. J., Shea D. E., “On the asymptotic behavior of the bounded solutions of some integral equations. II”, J. Math. Anal. Appl., 37:2 (1972), 288–306 | DOI | MR

[6] Levin J. J., Shea D. E., “On the asymptotic behavior of the bounded solutions of some integral equations. III”, J. Math. Anal. Appl., 37:3 (1972), 537–575 | DOI | MR | Zbl

[7] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P., Rutitskii Ya. B., Stetsenko V. Ya., Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969 | MR