Geodesic
On solvability of one class of Hammerstein nonlinear integral equations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2010), pp. 67-83 
A. Kh. Khachatryan; Kh. A. Khachatryan. On solvability of one class of Hammerstein nonlinear integral equations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2010), pp. 67-83. http://geodesic.mathdoc.fr/item/BASM_2010_2_a4/
@article{BASM_2010_2_a4,
     author = {A. Kh. Khachatryan and Kh. A. Khachatryan},
     title = {On solvability of one class of {Hammerstein} nonlinear integral equations},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {67--83},
     year = {2010},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2010_2_a4/}
}
TY  - JOUR
AU  - A. Kh. Khachatryan
AU  - Kh. A. Khachatryan
TI  - On solvability of one class of Hammerstein nonlinear integral equations
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2010
SP  - 67
EP  - 83
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/BASM_2010_2_a4/
LA  - en
ID  - BASM_2010_2_a4
ER  - 
%0 Journal Article
%A A. Kh. Khachatryan
%A Kh. A. Khachatryan
%T On solvability of one class of Hammerstein nonlinear integral equations
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2010
%P 67-83
%N 2
%U http://geodesic.mathdoc.fr/item/BASM_2010_2_a4/
%G en
%F BASM_2010_2_a4

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

The article deals with one class of Hammerstein nonlinear integral equations with kernel depending on the sum and the difference of arguments. In the particular case of basic nonlinear equation the existence of one parameter family of solutions is proved. Using special solution of this family the solution of basic nonlinear equation is constructed and asymptotic behavior at infinity is investigated. At the end of the work some of examples are given.

[1] Kufner A., Fuchik S., Nonlinear differential equations, Nauka, Moscow, 1988 (in Russian) | MR | Zbl

[2] Yengibaryan N. B., “On one nonlinear radiative transfer problem”, Astrophysica, 1966, no. 4, 31–36 (in Russian)

[3] Khachatryan Kh. A., “One parameter family of solutions for one class of Hammerstein nonlinear equations on a half line”, Doklady Mathematics, 80 (2009), 872–876 | DOI | MR | Zbl

[4] Yengibaryan N. B., Yengibaryan B. N., “Convolution type integral equation on a half line with completely monotonic kernel”, Math. sb., 187:10 (1996), 53–72 (in Russian) | DOI | MR | Zbl

[5] Arabadjyan L. G., “On one integral equation of transfer theory in nonhomogeneous medium”, Differential equations, 23 (1987), 1618–1622 (in Russian)

[6] Arabadjyan L. G., Yengibaryan N. B., “Convolution equations and nonlinear functional equations”, Itogi Nauki i Techniki. Ser. Mat. Anal., 22, 1984, 175–244 (in Russian) | MR | Zbl

[7] Kolmogorov A. N., Fomin V. S., Elements of functions theory and functional analysis, Moscow, 1981 (in Russian)