Journal of Mathematical Sciences

, Volume 208, Issue 6, pp 693–705 | Cite as

On One Two-Dimensional Linear Integral Equation with a Coefficient that has Zeros

  • D. ShulaiaEmail author


In this paper, we study, in the class of H¨older functions, linear two-dimensional integral equations with coefficients t that have zeros in the interval under consideration. Using the theory of singular integral equations, necessary and sufficient conditions for the solvability of these equations under some assumption on their kernels are given.


Integral Equation Homogeneous Equation Singular Integral Equation Fredholm Integral Equation Zero Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. H. Bareiss and I. K. Abu-Shumays, “On the structure of isotropic transport operators in space,” in: Transport Theory. Proc. Symp. Appl. Math., New York, 1967, SIAM-AMS Proc., 1, Am. Math. Soc., Providence, Rhode Island (1969), pp. 37–78Google Scholar
  2. 2.
    G. R. Bart and R. L. Warnock, “Linear integral equations of the third kind,” SIAM J. Math. Anal., 4, 609–622 (1973).MathSciNetCrossRefGoogle Scholar
  3. 3.
    I. A. Fel’dman, “The discrete spectrum of the characteristic equation of radiation transfer theory,” Mat. Issled., 10, No. 1 (35), 236–243, 301 (1975).Google Scholar
  4. 4.
    N. I. Muskhelishvili, Singular Integral Equations. Boundary Problems of Function Theory and Their Application to Mathematical Physics, Noordhoff, Groningen (1953).Google Scholar
  5. 5.
    E. Picard, “Sur les ‘equations int’egrales de troisi’eme esp’ece,” Ann. Sci. Ecole Norm. Sup. (3), 28, 459–472 (1911).Google Scholar
  6. 6.
    D. A. Shulaia, “Completeness theorems in linear multivelocity transport theory,” Dokl. Akad. Nauk SSSR, 259, No. 2, 332–335 (1981).MathSciNetGoogle Scholar
  7. 7.
    D. A. Shulaia, “A linear equation of multivelocity transport theory,” Zh. Vychisl. Mat. Mat. Fiz., 23, No. 5, 1125–1140 (1983).Google Scholar
  8. 8.
    D. A. Shulaia, “Inverse problem of linear multivelocity transport theory,” Dokl. Akad. Nauk SSSR, 270, No. 1, 82–87 (1983).MathSciNetGoogle Scholar
  9. 9.
    D. A. Shulaia, “Expansion of solutions of the equation of linear multivelocity transport theory in eigenfunctions of the characteristic equation,” Dokl. Akad. Nauk SSSR, 310, No. 4, 844–849 (1990).Google Scholar
  10. 10.
    D. Shulaia, “On one Fredholm integral equation of third kind,” Georgian Math. J., 4, No. 5, 461–476 (1997).MathSciNetCrossRefGoogle Scholar
  11. 11.
    D. Shulaia, “Solution of a linear integral equation of third kind,” Georgian Math. J., 9, No. 1, 179–196 (2002).MathSciNetGoogle Scholar
  12. 12.
    Ya. D. Tamarkin, “On Fredholm’s integral equations whose kernels are analytic in a parameter,” Ann. Math. (2), 28, Nos. 1–4, 127–152 (1926/27).Google Scholar
  13. 13.
    F. G. Tricomi, Integral Equations, Pure Appl. Math., 5, Interscience Publishers, New York–London (1957).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.I. Vekua Institute of Applied Mathematics of I. Javakhishvili Tbilisi State UniversityTbilisiGeorgia

Personalised recommendations