Boundary-value problems for weakly singular integral equations

Abstract

<p style='text-indent:20px;'>We consider a perturbed linear boundary-value problem for a weakly singular integral equation. Assume that the generating boundary-value problem is unsolvable for arbitrary inhomogeneities. Efficient conditions for the coefficients guaranteeing the appearance of the family of solutions of the perturbed linear boundary-value problem in the form of Laurent series in powers of a small parameter <inline-formula><tex-math id="M1">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> with singularity at the point <inline-formula><tex-math id="M2">\begin{document}$ \varepsilon = 0 $\end{document}</tex-math></inline-formula> are established.</p>