V. S. Vladimirov, “Solutions of $p$-adic string equations”, TMF, 167:2 (2011), 163–170; Theoret. and Math. Phys., 167:2 (2011), 539

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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 167, Number 2, Pages 163–170
DOI: https://doi.org/10.4213/tmf6631 (Mi tmf6631)

This article is cited in 21 scientific papers (total in 21 papers)

Solutions of

p

$p$ -adic string equations

V. S. Vladimirov

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Full-text PDF (490 kB) Citations (21)

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DOI: https://doi.org/10.4213/tmf6631

Abstract: We review several purely mathematical results concerning boundary value problems for nonlinear pseudodifferential equations for

p

$p$ -adic closed and open strings in the tree approximation in the case

d = 1

$d=1$ . For the solutions of these problems, we present formulas establishing the relations between the numbers of their zeros, the multiplicities of the zeros, and the numbers indicating how many times the solutions change sign.

Keywords:

p

$p$ -adic string.

Received: 13.10.2010

English version:
Theoretical and Mathematical Physics, 2011, Volume 167, Issue 2, Pages 539–546
DOI: https://doi.org/10.1007/s11232-011-0040-z

Bibliographic databases:

Document Type: Article

UDC: 2

Language: Russian

Citation: V. S. Vladimirov, “Solutions of

p

$p$ -adic string equations”, TMF, 167:2 (2011), 163–170; Theoret. and Math. Phys., 167:2 (2011), 539–546

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf6631

https://doi.org/10.4213/tmf6631

https://www.mathnet.ru/eng/tmf/v167/i2/p163

This publication is cited in the following 21 articles:

Kh. A. Khachatryan, H. S. Petrosyan, “On qualitative properties of the solution of a boundary value problem for a system of nonlinear integral equations”, Theoret. and Math. Phys., 218:1 (2024), 145–162
Kh. A. Khachatryan, H. S. Petrosyan, “An iterative method for solving one class of non-linear integral equations with Nemytskii operator on the positive semi-axis”, Izv. Math., 88:4 (2024), 760–793
Paolo Aniello, Stefano Mancini, Vincenzo Parisi, “Quantum mechanics on a p-adic Hilbert space: Foundations and prospects”, Int. J. Geom. Methods Mod. Phys., 21:10 (2024)
H. S. Petrosyan, Kh. A. Khachatryan, “Uniqueness of the Solution of a Class of Integral Equations with Sum-Difference. Kernel and with Convex Nonlinearity on the Positive Half-Line”, Math. Notes, 113:4 (2023), 512–524
A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan, “On nonlinear convolution-type integral equations in the theory of $p$-adic strings”, Theoret. and Math. Phys., 216:1 (2023), 1068–1081
Kh. A. Khachatryan, H. S. Petrosyan, “On non-trivial solvability of one system of non-linear integral equations on the real axis”, Izv. Math., 87:5 (2023), 1062–1077
Wenbing Wu, “Uniqueness and stability analysis to a system of nonlocal partial differential equations related to an epidemic model”, Math Methods in App Sciences, 46:8 (2023), 8445
Kh.A. Khachatryan, H.S. Petrosyan, A. R. Hakobyan, “On solvability of one class of integral equations on whole line with monotonic and convex nonlinearity”, J Math Sci, 271:5 (2023), 610
B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, “On the Occasion of the Centenary of the Birth of V. S. Vladimirov (1923–2012)”, P-Adic Num Ultrametr Anal Appl, 15:3 (2023), 243
Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022) (to appear)
Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022), 446–479
A. Kh. Khachatryan, Kh. A. Khachatryan, “Ob odnoi sisteme integralnykh uravnenii na vsei pryamoi s vypukloi i monotonnoi nelineinostyu”, Proceedings of NAS RA. Mathematics, 2022, 65
A. Kh. Khachatryan, Kh. A. Khachatryan, “A System of Integral Equations on the Entire Axis with Convex and Monotone Nonlinearity”, J. Contemp. Mathemat. Anal., 57:5 (2022), 311
Kh. A. Khachatryan, H. S. Petrosyan, “On One Class of Multidimensional Integral Equations of Convolution Type with Convex Nonlinearity”, Diff Equat, 58:5 (2022), 680
Kh. A. Khachatryan, “O razreshimosti odnoi sistemy nelineinykh integralnykh uravnenii tipa Gammershteina na pryamoi”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 19:2 (2019), 164–181
A. Kh. Khachatryan, Kh. A. Khachatryan, “On the Solvability of Some Nonlinear Integral Equations in Problems of Epidemic Spread”, Proc. Steklov Inst. Math., 306 (2019), 271–287
Kh. A. Khachatryan, “On the solubility of certain classes of non-linear integral equations in $p$-adic string theory”, Izv. Math., 82:2 (2018), 407–427
Kh. A. Khachatryan, A. S. Petrosyan, M. O. Avetisyan, “Voprosy razreshimosti odnogo klassa nelineinykh integralnykh uravnenii tipa svertki v $\mathbb {R}^n$”, Tr. IMM UrO RAN, 24, no. 3, 2018, 247–262
Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121
I. V. Volovich, V. Zh. Sakbaev, “Universal boundary value problem for equations of mathematical physics”, Proc. Steklov Inst. Math., 285 (2014), 56–80

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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