Integral equations of the third kind for the case of piecewise monotone coefficients

We examine the third kind integral equations in Hölder class. The coefficients of the equations are piecewise strictly monotone functions having simple zeros. By singular integral equations theory, for solvability of considered equations, we give the necessary and sufficient conditions. Finding a solution is reduced to solving a regular integral equation of second kind. Keywords: Piecewise, Eigenvalues, Holomorphic, Singular operato