Geodesic
On solvability of an infinite nonlinear system of algebraic equations with Teoplitz–Hankel matrices
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 158-167.

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

In the present paper a special class of infinite nonlinear system of algebraic equations with Teoplitz–Hankel matrices is studied. Above mentioned class of equations has direct applications in radiative transfer theory. Existence componentwise positive solutions for the system in space $l_1$ are proved and some examples for mentioned equations, representing separate interest are given.
Keywords: Teoplitz–Hankeltypematrices, iteration, limit of solution.
Mots-clés : positive solution 
@article{UZERU_2017_51_2_a3,
     author = {Kh. A. Khachatryan and M. H. Avetisyan},
     title = {On solvability of an infinite nonlinear system of algebraic equations with {Teoplitz{\textendash}Hankel} matrices},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {158--167},
     publisher = {mathdoc},
     volume = {51},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a3/}
}
TY  - JOUR
AU  - Kh. A. Khachatryan
AU  - M. H. Avetisyan
TI  - On solvability of an infinite nonlinear system of algebraic equations with Teoplitz–Hankel matrices
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2017
SP  - 158
EP  - 167
VL  - 51
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a3/
LA  - en
ID  - UZERU_2017_51_2_a3
ER  - 
%0 Journal Article
%A Kh. A. Khachatryan
%A M. H. Avetisyan
%T On solvability of an infinite nonlinear system of algebraic equations with Teoplitz–Hankel matrices
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2017
%P 158-167
%V 51
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a3/
%G en
%F UZERU_2017_51_2_a3
Kh. A. Khachatryan; M. H. Avetisyan. On solvability of an infinite nonlinear system of algebraic equations with Teoplitz–Hankel matrices. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 51 (2017) no. 2, pp. 158-167. http://geodesic.mathdoc.fr/item/UZERU_2017_51_2_a3/

[1] N. B. Engibaryan, “A Nonlinear Problem of Radiative Transfer”, Astrophysics, 1:3 (1965), 158–159 (in Russian) | DOI

[2] N. B. Engibaryan, “A Discrete Model for Nonlinear Problems of Radiation Transfer: Principle of Invariance and Factorization”, Mathematical Models and Comp. Simulations, 27:5 (2015), 127–136 | MR | 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 (in Russian) | DOI | MR | Zbl

[4] V.S. Vladimirov, Volovich Ya.I. Volovich, “Nonlinear Dynamics Equation in $p$-Adic String Theory”, Theoret. and Math. Phys., 138:3 (2004), 297–309 | DOI | MR | Zbl

[5] V.S. Vladimirov, “The Equation of the $p$-Adic Open String for the Scalar Tachyon Field”, Izv. Mathematics, 69:3 (2005), 487–512 | DOI | MR | Zbl

[6] Kh. A. Khachatryan, M. F. Broyan, “One-Parameter Family of Positive Solutions for a Class of Nonlinear Infinite Algebraic System with Teoplitz–Hankel Type Matrices”, Journal of Contemporary Mathematical Analysis, 48:5 (2013), 189–200 | DOI | MR

[7] A. Kh. Khachatryan, A. K. Kroyan, “On the Positive Solvability of an Infinite System of Nonlinear Algebraic Equations in $l_1$ with Teoplitz Matrices”, Vestnik RAU. Phys. Math. Science, 2015, no. 1, 16–25 (in Russian)

[8] H. H. Azizyan, Kh. A. Khachatryan, “One-Parametric Family of Positive Solutions for a Class of Nonlinear Discrete Hammerstein–Volterra Equations”, Ufa Mathematical Journal, 8:1 (2016,), 13–19 (in Russian) | DOI | MR

[9] H. S. Petrosyan, M. G. Kostanyan, “On Solvability of an Class of Nonlinear Infinity Systems of Algebraic Equations with the Teoplitz Matrices”, Mathematics in Higher School, 10:1 (2014), 35–40 (in Russian)

[10] L. G. Arabadzyan, “On Discrete Wiener–Hopf Equations in the Conservative Case”, Math. Analysis and Applications (Armenian State Ped. University after Kh. Abovyan), 1980, 26–36 (in Russian)

[11] Kh.A. KhachatryanOn Nontrivial Solutions of a Class Convolution Type Nonlinear Integral Equations, VI Russian-Armenian Conferance on Mathematical Physics and Analitical Mechanics (Rostov-on-Don), 2016, 40–41 (in Russian)