Asymptotic behavior of a solution for one class of nonlinear integro-differential equations in the income distribution problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 1, pp. 188-206 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We study a class of nonlinear integro-differential equations of convolution type, which have direct application in econometrics. Some qualitative properties of the solution are studied: its asymptotic behavior, monotonicity, and smoothness. A specific example of an applied nature is given.
Keywords: wealth distribution, asymptotics, monotonicity.
Mots-clés : wavefront, solution limit
@article{TIMM_2021_27_1_a17,
     author = {A. Kh. Khachatryan and Kh. A. Khachatryan and H. S. Petrosyan},
     title = {Asymptotic behavior of a solution for one class of nonlinear integro-differential equations in the income distribution problem},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {188--206},
     year = {2021},
     volume = {27},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2021_27_1_a17/}
}
TY  - JOUR
AU  - A. Kh. Khachatryan
AU  - Kh. A. Khachatryan
AU  - H. S. Petrosyan
TI  - Asymptotic behavior of a solution for one class of nonlinear integro-differential equations in the income distribution problem
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2021
SP  - 188
EP  - 206
VL  - 27
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMM_2021_27_1_a17/
LA  - ru
ID  - TIMM_2021_27_1_a17
ER  - 
%0 Journal Article
%A A. Kh. Khachatryan
%A Kh. A. Khachatryan
%A H. S. Petrosyan
%T Asymptotic behavior of a solution for one class of nonlinear integro-differential equations in the income distribution problem
%J Trudy Instituta matematiki i mehaniki
%D 2021
%P 188-206
%V 27
%N 1
%U http://geodesic.mathdoc.fr/item/TIMM_2021_27_1_a17/
%G ru
%F TIMM_2021_27_1_a17
A. Kh. Khachatryan; Kh. A. Khachatryan; H. S. Petrosyan. Asymptotic behavior of a solution for one class of nonlinear integro-differential equations in the income distribution problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 1, pp. 188-206. http://geodesic.mathdoc.fr/item/TIMM_2021_27_1_a17/

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

[2] Bellman R., Kuk K.L., Differentsialno-raznostnye uravneniya, Mir, M., 1967, 548 pp.

[3] Mondelbrot B., “The Pareto-Levy law and distribution of income”, Int. Economic Rev., 1:2 (1960), 79–106 | DOI

[4] Champernowne D.G., “A model of income distribution”, Economic J., 63:250 (1953), 318–351 | DOI

[5] Chen Yu, Liao Yujie, Zhang Qi and Zhang Weiping, “Ruin probabilities for the phase-type dual model perturbed by diffusion”, Communications in Statistics - Theory and Methods, 2020, 1–19 | DOI

[6] Daliri Birjandi M.H., Saberi-Nadjafi J., Ghorbani A., “An efficient numerical method for a class of nonlinear Volterra integro-differential equations”, J. Appl. Math., 2018, 7461058, 7 pp. | DOI | MR | Zbl

[7] Khachatryan A.Kh., Khachatryan Kh.A., “Ob odnom integro-differentsialnom uravnenii v zadache raspredeleniya bogatstva strany”, Ekonomika i mat. metody TsEMI RAN, 45:4 (2009), 84–96

[8] Khachatryan A.Kh., Khachatryan Kh.A., “O razreshimosti odnogo nelineinogo integro-differentsialnogo uravneniya v zadache raspredeleniya dokhoda”, Zhurn. vychislit. matematiki i mat. fiziki, 50:10 (2010), 1793–1802 | MR | Zbl

[9] Khachatryan A.Kh., Khachatryan Kh.A., “On solvability of a nonlinear problem in theory of income distribution”, Eurasian Math. J., 2:2 (2011), 75–88 | MR | Zbl

[10] Kolmogorov A.N., Fomin V.S., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1980, 542 pp. | MR

[11] Khachatryan Kh.A., Petrosyan A.S., “O razreshimosti odnogo klassa nelineinykh integralnykh uravnenii Gammershteina - Stiltesa na vsei pryamoi”, Tr. MIAN, 308 (2020), 253–264 | Zbl

[12] Diekmann O., “Thresholds and travelling waves for the geographical spread of infection”, J. Math. Biol., 6:2 (1978), 109–130 | DOI | MR | Zbl

[13] Diekmann O., “Run for your life. A note on the asymptotic speed of propagation of an epidemic”, J. Diff. Eq., 33:1 (1979), 58–73 | DOI | MR | Zbl

[14] Diekmann Odo, Kaper Hans G., “On the bounded solutions of a nonlinear convolution equation”, Nonlinear Analysis: Theory, Methods Application, 2:6 (1978), 721–737 | DOI | MR | Zbl

[15] Diekmann Odo, Gyllenberg Mats, “Equations with infinite delay: blending the abstract and the concrete”, J. Diff. Eq., 252:2 (2012), 819–851 | DOI | MR | Zbl

[16] Budak B.M., Fomin S.V., Kratnye integraly i ryady, Nauka, M., 1965, 608 pp. | MR

[17] Gevorkyan G.G., Engibaryan N.B., “Novye teoremy dlya integralnogo uravneniya vosstanovleniya”, Izv. NAN Armenii. Matematika, 32:1 (1997), 5–20 | MR | Zbl

[18] Engibaryan N.B., “Uravneniya vosstanovleniya na poluosi”, Izv. RAN. Ser. matematicheskaya, 63:1 (1999), 61–76 | MR | Zbl

[19] Rudin U., Funktsionalnyi analiz, Mir, M., 1975, 444 pp.

[20] Polia G. , Sege G., Zadachi i teoremy iz analiza, Ch. 1, Nauka, M., 1978, 392 pp. | MR