# On One Linear Integral Equation with a Coefficient that has Zeros

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## Abstract

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.

## Keywords

Integral Equation Homogeneous Equation Singular Integral Equation Singular Integral Operator Zero Solution
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