Geodesic
The existence of odd solution for one boundary-value problem with power nonlinearity
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 4, pp. 88-96 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the present work we investigate a boundary value problem for a nonlinear convolution type singular integral equation on the whole axis with power nonlinearity. The above-mentioned problem has direct application in $p$-adic open-closed strings theory. We prove the existence of a rolling odd solution for the considered problem. We also establish an integral asymptotic for the constructed solution. At the end we list particular examples of the given equation, having separate interest.
Keywords: nonlinear equation, iteration, limit of solution, boundary value problem. 
@article{VNGU_2018_18_4_a6,
     author = {Kh. A. Khachatryan and A. K. Kroyan},
     title = {The existence of odd solution for one boundary-value problem with power nonlinearity},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {88--96},
     year = {2018},
     volume = {18},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2018_18_4_a6/}
}
TY  - JOUR
AU  - Kh. A. Khachatryan
AU  - A. K. Kroyan
TI  - The existence of odd solution for one boundary-value problem with power nonlinearity
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2018
SP  - 88
EP  - 96
VL  - 18
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VNGU_2018_18_4_a6/
LA  - ru
ID  - VNGU_2018_18_4_a6
ER  - 
%0 Journal Article
%A Kh. A. Khachatryan
%A A. K. Kroyan
%T The existence of odd solution for one boundary-value problem with power nonlinearity
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2018
%P 88-96
%V 18
%N 4
%U http://geodesic.mathdoc.fr/item/VNGU_2018_18_4_a6/
%G ru
%F VNGU_2018_18_4_a6
Kh. A. Khachatryan; A. K. Kroyan. The existence of odd solution for one boundary-value problem with power nonlinearity. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 4, pp. 88-96. http://geodesic.mathdoc.fr/item/VNGU_2018_18_4_a6/

[1] Volovich I. V., “$p$-Adic String”, Classical Quantum Gravity, 4:4 (1987), L83–L87 | DOI | MR

[2] Brekke L., Freund P. G. O., Olson M., Witten E., “Non-Archimedean String Dynamics”, Nuclear Phys. B, 302:3 (1988), 365–402 | DOI | MR

[3] Frampton P. H., Okada Y., “Effective Scalar Field Theory of $p$-Adic String”, Phys. Rev. D, 37:10 (1989), 3077–3079 | DOI | MR

[4] Brekke L., Freund P. G. O., “$p$-Adic Numbers in Physics”, Physics Reports, 233:1 (1993), 1–66 | DOI | MR

[5] Moeller N., Schnabl M., “Tachyon Condensation in Open-Closed $p$-Adic String Theory”, J. of High Energy Physics, 2004:01 (2004), 18 | DOI | MR

[6] V. S. Vladimirov, “Nonlinear equations for $p$-adic open, closed, and open-closed strings”, Theor. and Math. Phys., 149:3 (2006), 1604–1616 | DOI | DOI | MR | Zbl

[7] V. S. Vladimirov, “Nonexistence of solitions of the $p$-adic strings”, Theor. and Math. Phys., 174:2 (2013), 178–185 | DOI | DOI | MR | Zbl

[8] Kh. A. Khachatryan,, “On the solubility of sertain classes of non-linear integral equations in $p$-adic string theory”, Izv. Math., 82:2 (2018), 407–427 | DOI | DOI | MR | Zbl

[9] Kh. A. Khachatryan, H. S. Petrosyan, “One-parameter families of positive solutions of some classes of nonlinear convolution type integrasl equations”, Sib. J. Pure and Appl. Math., 231:2 (2018), 153–167 | MR | Zbl

[10] Kh. A. Khachatryan, “Positive solubility of some classes of non-linear integral equations of Hammerstein type on the semi-axis and on the whole line”, Izv. Math., 79:2 (2015), 411–430 | DOI | DOI | MR | Zbl

[11] A. N. Kolmogorov, Elements of the Theory of Functions and Functional Analysis, Dover Books on Mathematics, 1999

[12] L. G. Arabadzhyan, A. S. Khachatryan, “A class of integral equations of convolution type”, Sbornik: Mathematics, 198:7 (2007), 949–966 | DOI | DOI | MR | Zbl

[13] N. B. Engibaryan, “Renewal equations on the semi-axis”, Izv. Math., 63:1 (1999), 57–71 | DOI | DOI | MR | Zbl