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On One Two-Dimensional Linear Integral Equation with a Coefficient that has Zeros

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Abstract

In this paper, we study, in the class of H¨older functions, linear two-dimensional integral equations with coefficients t that have zeros in the interval under consideration. Using the theory of singular integral equations, necessary and sufficient conditions for the solvability of these equations under some assumption on their kernels are given.

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Authors and Affiliations

  1. I. Vekua Institute of Applied Mathematics of I. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    D. Shulaia

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  1. D. Shulaia
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Correspondence to D. Shulaia.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 90, Differential Equations and Mathematical Analysis, 2014.

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Shulaia, D. On One Two-Dimensional Linear Integral Equation with a Coefficient that has Zeros. J Math Sci 208, 693–705 (2015). https://doi.org/10.1007/s10958-015-2478-2

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  • DOI: https://doi.org/10.1007/s10958-015-2478-2

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