Journal of Mathematical Sciences

, Volume 208, Issue 6, pp 706–722 | Cite as

On One Linear Integral Equation with a Coefficient that has Zeros

  • D. ShulaiaEmail author
  • P. Ghurtskaia


The aim of this paper is to study, in the class of H¨older functions, a linear integral equation with coefficient having two simple zeros in the interval under consideration. Using the theory of singular integral equations, we give the necessary and sufficient conditions for the solvability of this equation under some assumptions on their kernel. Finding a solution is reduced to solving a regular integral equation of the second kind.


Integral Equation Homogeneous Equation Singular Integral Equation Singular Integral Operator Zero Solution 
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© Springer Science+Business Media New York 2015

Authors and Affiliations

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

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