Abstract
We consider a singularly perturbed Fredholm integro-differential equation with a rapidly varying kernel. We derive an algorithmfor constructing regularized asymptotic solutions. It is shown that, given a rapidly decreasing multiplier of the kernel, the original problem does no involve the spectrum (i.e., it is solvable for any right-hand side).
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Original Russian Text © A. A. Bobodzhanov, V. F. Safonov, 2009, published in Matematicheskie Zametki, 2009, Vol. 85, No. 2, pp. 163–179.
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Bobodzhanov, A.A., Safonov, V.F. “Splashes” in Fredholm integro-differential equations with rapidly varying kernels. Math Notes 85, 153–167 (2009). https://doi.org/10.1134/S0001434609010192
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DOI: https://doi.org/10.1134/S0001434609010192