We establish conditions for the existence of solutions of boundary-value problems with control for the Fredholm integral equations with degenerate kernels in Banach spaces and determine the general form of these solutions. We also find the general form of control for which these solutions exist. The problem is solved by using the theory of generalized inversion of Fredholm integral operators with degenerate kernels in Banach spaces and pseudoinversion of Fredholm integral operators with degenerate kernels in finite-dimensional spaces.
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Translated from Neliniini Kolyvannya, Vol. 24, No. 1, pp. 83–98, January–March, 2021.
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Zhuravlev, V.P., Fomin, N.P. Boundary-Value Problems with Control for Fredholm Integral Equations with Degenerate Kernels in Banach Spaces. J Math Sci 265, 651–668 (2022). https://doi.org/10.1007/s10958-022-06076-4
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DOI: https://doi.org/10.1007/s10958-022-06076-4