Geodesic
On some classes of nonlinear integral equations with noncompact operators
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 130 (2013) no. 1, pp. 181-188

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

The work is devoted to the investigation of some classes of nonlinear integral equations of Hammerstein–Nemitski type with noncompact operators. Above mentioned class of equations, beside the theoretical interest has immediately an application in kinetic theory of gases. The existence theorems for positive solutions in different functional spaces are proved.
Keywords: Hammerstein–Nemitski type integral equation, condition of conservativity, Caratheodory's condition, monotonicity, Wiener–Hopf equation. 
Kh. A. Khachatryan. On some classes of nonlinear integral equations with noncompact operators. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 130 (2013) no. 1, pp. 181-188. http://geodesic.mathdoc.fr/item/VSGTU_2013_130_1_a16/
@article{VSGTU_2013_130_1_a16,
     author = {Kh. A. Khachatryan},
     title = {On some classes of nonlinear integral equations with noncompact operators},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {181--188},
     year = {2013},
     volume = {130},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2013_130_1_a16/}
}
TY  - JOUR
AU  - Kh. A. Khachatryan
TI  - On some classes of nonlinear integral equations with noncompact operators
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2013
SP  - 181
EP  - 188
VL  - 130
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2013_130_1_a16/
LA  - ru
ID  - VSGTU_2013_130_1_a16
ER  - 
%0 Journal Article
%A Kh. A. Khachatryan
%T On some classes of nonlinear integral equations with noncompact operators
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2013
%P 181-188
%V 130
%N 1
%U http://geodesic.mathdoc.fr/item/VSGTU_2013_130_1_a16/
%G ru
%F VSGTU_2013_130_1_a16

[1] N. B. Engibaryan, A. Kh. Khachatryan, “On nonlinear theory dynamics of dilute gas”, Matem. Mod., 16:1 (2004), 67–74 | MR | Zbl

[2] C. Cercignani, Theory and application of the Boltzmann equation, Scottish Academic Press, Edinburg, London, 1975, 415 pp. ; K. Cherchinyani, Teoriya i prilozheniya uravneniya Boltsmana, Mir, M., 1978, 495 pp. | Zbl

[3] A. Kh. Khachatryan, Kh. A. Khachatryan, “Qualitative difference between solutions for a model of the Boltzmann equation in the linear and nonlinear cases”, Theoret. and Math. Phys., 172:3 (2012), 1315–1320 | DOI | DOI | Zbl

[4] P. S. Milojević, “A global description of solutions to nonlinear perturbations of the Wiener–Hopf integral equations”, Electronic Journal of Differential Equations (EJDE), 2006 (2006), 51, 14 pp. | Zbl

[5] Kh. A. Khachatryan, “One-parameter family of solutions for one class of hammerstein nonlinear equations on a half-line”, Dokl. Math., 80:3 (2009), 872–876 | DOI | Zbl

[6] R. Precup, Methods in nonlinear integral equations, Springer Verlag, New York, 2007, 232 pp.

[7] C. D. Panchal, “Existence theorems for equation of Hammerstein type”, Quart. J. Math., 35:3 (1984), 311–319 | DOI | Zbl

[8] A. Kh. Khachatryan, Kh. A. Khachatryan, “On an integral equation with monotonic nonlinearity”, Mem. Differential and Equations Math. Phys., 51 (2010), 59–72 pp. | Zbl

[9] Kh. A. Khachatryan, “On a class of integral equations of Urysohn type with strong non-linearity”, Izv. Math., 76:1 (2012), 163–189 | DOI | DOI | MR | Zbl

[10] G. Emmanuele, “An existense theorem for Hammerstein integral equations”, Portugaliae Mathematica, 51:4 (1994), 607–611 | Zbl

[11] A. Kh. Khachatryan, Kh. A. Khachatryan, “A nonlinear integral equation of Hammerstein type with a noncompact operator”, Sb. Math., 201:4 (2010), 595–606 | DOI | DOI | MR | Zbl | Zbl

[12] L. G. Arabadzhyan, “Existence of nontrivial solutions of some linear and nonlinear equations of convolution type”, Ukrainian Math. J., 41:12 (1989), 1359–1367 | DOI | Zbl

[13] L. G. Arabadzhyan, N. B. Engibaryan, “Convolution equations and nonlinear functional equations”, J. Soviet Math., 36:6 (1987), 745–791 | DOI | MR | Zbl | Zbl

[14] A. N. Kolmogorov, S. V. Fomin, Elements of the theory of functions and functional analysis, Nauka, Moscow, 1981, 544 pp.