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On the Constructive Solvability of a Two-Dimensional Nonlinear Integral Equation Arising in the Theory of \(p\)-Adic Strings

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Abstract

This paper is devoted to the study of existence and uniqueness of the solution of a class of nonlinear two-dimensional integral equations in the plane. Such equations arise in theory of \(p\)-adic strings. In addition, equations of this nature are encountered in mathematical epidemiology. Constructive existence and uniqueness theorems for a positive bounded solution are proved. We also obtain the integral asymptotic of the solution. At the end of the paper applied examples of this equation are given.

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References

  1. I. Ya. Arefeva, B. G. Dragovic and I. V. Volovich, “Open and closed \(p\)-adic strings and quadratic extensions of number fields,” Phys. Lett. B 212 (3), 283–291 (1988).

    Article  MathSciNet  Google Scholar 

  2. V. S. Vladimirov, “Nonlinear equations for \(p\)-adic open, closed, and open-closed strings,” Theor. Math. Phys. 149 (3), 1604–1616 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  3. V. S. Vladimirov and Ya. I. Volovich, “Nonlinear dynamics equation in \(p\)-adic string theory,” Theor. Math. Phys. 138 (3), 297–309 (2004).

    Article  MATH  Google Scholar 

  4. O. Diekmann, “Threshold and travelling waves for the geographical spread of infection,” J. Math. Biol. 6, 109–130 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  5. O. Diekmann, “Run for your life. A note on the asymptotic speed of propagation of an epidemic,” J. Diff. Equat. 33 (1), 58–73 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  6. Kh. A. Khachatryan and H. S. Petrosyan, “On solvability of a class of multidimensional integral equation in the mathematical theory of geographic distributuion of an epidemic,” J. Contemp. Math. Anal. 56 (3), 143–157 (2021).

    Article  MATH  Google Scholar 

  7. Kh. A. Khachatryan, “Solvability of some nonlinear boundary value problems for singular integral equations of convolution type,” Trans. Moscow Math. Soc. 81 (1), 1–31 (2020).

    MathSciNet  MATH  Google Scholar 

  8. Kh. A. Khachatryan and H. S. Petrosyan, “Alternating bounded solutions of a class of nonlinear two-dimensional convolution-type integral equations,” Trans. Moscow Math. Soc. 82, 259–271 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  9. Kh. A. Khachatryan and H. S. Petrosyan, “On one class of multidimensional integral equations of convolution type with convex nonlinearity,” Diff. Equat. 58 (5), 680–690 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  10. W. Rudin, Functional Analysis (McGraw-Hill, New York, 1973).

    MATH  Google Scholar 

  11. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, 1976) [in Russian].

    Google Scholar 

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Funding

This work was supported by the Russian Scientific Foundation (Project no. 19–11–00223).

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Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian, Yerevan, 0025, Republic of Armenia

    Kh. A. Khachatryan

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, 1 Leninskiye Gory, Main Building, Moscow, 119991, Russian Federation

    Kh. A. Khachatryan

  3. Armenian National Agrarian University, Teryan 74, Yerevan, 0009, Republic of Armenia

    H. S. Petrosyan

  4. Department of Higher Mathematics, Physics and Applied Mechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, 1 Leninskiye Gory, Main Building, Moscow, 119991, Russian Federation

    H. S. Petrosyan

Authors
  1. Kh. A. Khachatryan
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  2. H. S. Petrosyan
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Correspondence to Kh. A. Khachatryan or H. S. Petrosyan.

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Khachatryan, K.A., Petrosyan, H.S. On the Constructive Solvability of a Two-Dimensional Nonlinear Integral Equation Arising in the Theory of \(p\)-Adic Strings. P-Adic Num Ultrametr Anal Appl 14 (Suppl 1), S74–S82 (2022). https://doi.org/10.1134/S2070046622050065

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  • DOI: https://doi.org/10.1134/S2070046622050065

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