We study quasilinear systems of integral equations that are linear with respect to the principal part and nonlinear with respect to the integral term. We formulate sufficient conditions for the local existence of a unique smooth solution to such a system in terms of matrix pencils and provide some examples. We study quasilinear systems of integral equations that are linear with respect to the principal part and nonlinear with respect to the integral term. We formulate sufficient conditions for the local existence of a unique smooth solution to such a system in terms of matrix pencils and provide some examples.
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Bulatov, M., Solovarova, L. Solvability of Quasilinear Integral–Algebraic Equations. J Math Sci 279, 756–762 (2024). https://doi.org/10.1007/s10958-024-07057-5
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DOI: https://doi.org/10.1007/s10958-024-07057-5