Skip to main content
SpringerLink
Log in

On solvability of one class of nonlinear integral equations on whole line with a weak singularity at zero

  • Research Articles
  • Published:
p-Adic Numbers, Ultrametric Analysis and Applications Aims and scope Submit manuscript

Abstract

In present work we investigate one class of nonlinear integral equations with singularity at zero and boundary value conditions at ±∞. Above mentioned class of equations has direct applications in string theory and in the case of concrete structure of the kernel it describes the dynamics of the open-closed p-adic string for the scalar tachyon field. We prove the existence of nontrivial solution in a certain weight class of functions.With an additional restriction on the kernel the uniqueness of the obtained solution is proved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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 

  2. 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 

  3. V. S. Vladimirov, “The equation of the p-adic open string for the scalar tachyon field,” Izv. Math. 69 (3), 487–512 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  4. Kh. A. Khachatryan, “On nontrivial solutions of one class convolution type nonlinear integral equations,” VI Russian-Armenian Conference on Mathematical Physics and Analytical Mechanics, pp. 40–41 (Rostov on Don, 2016) [in Russian]. Available at: http://rus-arm.sfedu.ru/thethis.pdf.

    Google Scholar 

  5. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis (Nauka, Moscow, 1981).

    MATH  Google Scholar 

  6. L. G. Arabadzhyan and A. S. Khachatryan, “A class of integral equations of convolution type,” SbornikMath. 198 (7), 949–966 (2007).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Armenia, Armenia, Armenia

    Khachatur A. Khachatryan

Authors
  1. Khachatur A. Khachatryan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Khachatur A. Khachatryan.

Additional information

The text was submitted by the author in English.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khachatryan, K.A. On solvability of one class of nonlinear integral equations on whole line with a weak singularity at zero. P-Adic Num Ultrametr Anal Appl 9, 292–305 (2017). https://doi.org/10.1134/S2070046617040045

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2070046617040045

Key words

Search

Navigation