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Boundary-value problems for weakly singular integral equations

The present work was supported by the Grant H2020-MSCA-RISE-2019, project number 873071 (SOMPATY: Spectral Optimization: From Mathematics to Physics and Advanced Technology)

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  • 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 $ \varepsilon $ with singularity at the point $ \varepsilon = 0 $ are established.

    Mathematics Subject Classification: Primary: 45B05, 45E99; Secondary: 47G10.


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