Geodesic
On solvability of a nonlinear problem in theory of income distribution
Eurasian mathematical journal, Tome 2 (2011) no. 2, pp. 75-88 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a nonlinear integro-differential equation with a Hammerstein type noncompact operator, arising in the theory of income distribution. We prove the existence of a positive solution of the nonlinear problem in Sobolev space $W_1^1(\mathbb R^+)$. We list some examples arising in applications. For one modeling problem a uniqueness theorem is proved. At the end of the paper the results of numerical calculations are given. 
@article{EMJ_2011_2_2_a3,
     author = {A. Khachatryan and Kh. Khachatryan},
     title = {On solvability of a~nonlinear problem in theory of income distribution},
     journal = {Eurasian mathematical journal},
     pages = {75--88},
     year = {2011},
     volume = {2},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a3/}
}
TY  - JOUR
AU  - A. Khachatryan
AU  - Kh. Khachatryan
TI  - On solvability of a nonlinear problem in theory of income distribution
JO  - Eurasian mathematical journal
PY  - 2011
SP  - 75
EP  - 88
VL  - 2
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a3/
LA  - en
ID  - EMJ_2011_2_2_a3
ER  - 
%0 Journal Article
%A A. Khachatryan
%A Kh. Khachatryan
%T On solvability of a nonlinear problem in theory of income distribution
%J Eurasian mathematical journal
%D 2011
%P 75-88
%V 2
%N 2
%U http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a3/
%G en
%F EMJ_2011_2_2_a3
A. Khachatryan; Kh. Khachatryan. On solvability of a nonlinear problem in theory of income distribution. Eurasian mathematical journal, Tome 2 (2011) no. 2, pp. 75-88. http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a3/

[1] L. G. Arabadjyan, N. B. Yengibaryan, “Convolution equations and nonlinear functional equations”, Itogi nauki i techniki, Math. analys, 22, 1984, 175–244 (in Russian) | MR | Zbl

[2] L. G. Arabadjyan, “On one integral equation of Radiative transfer theory in nonhomogeneous medium”, Diff. equation, 23:9 (1987), 1619–1622

[3] J. Banas, “Integhrable solutions of Hammerstein and Urysohn integral equations”, J. Austral. Math. Soc. (A), 46 (1989), 61–68 | DOI | MR | Zbl

[4] H. Brezis, F. E. Browder, “Existence theorems for nonlinear integral equations of Hammerstein type”, Bull. Amer. Math. Soc., 81:1 (1975), 73–78 | DOI | MR | Zbl

[5] G. Emmanuele, “An existense theorem for Hammershtein integral equations”, Portugal Mathem., 51:4 (1994), 607–611 | MR | Zbl

[6] A. Kh. Khachatryan, Kh. A. Khachatryan, “On a integro-differential equation in the problem of wealth distribution”, J. Economics and Mathematical Methods, 45:4 (2009), 84–96 (in Russian)

[7] Kh. A. Khachatryan, E. A. Khachatryan, “On solvability some classes of nonlinear integro-differential equations with noncompact operator”, Russian mathematics, 55:1 (2011), 91–100 | DOI | MR | Zbl

[8] M. A. Krasnoselski, Positive solutions of operator equations, Nauka, Moscow, 1962 (in Russian) | MR

[9] I. D. Sargan, “The distribution of wealth”, Econometrics, 25:4 (1957), 568–590 | DOI | MR | Zbl