Geodesic
“Splashes” in Fredholm Integro-Differential Equations with Rapidly Varying Kernels
Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 163-179 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a singularly perturbed Fredholm integro-differential equation with a rapidly varying kernel. We derive an algorithm for 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).
Keywords: integro-differential equation, splash function, Fredholm operator, Volterra operator, regularization of an integral, boundary layer.
Mots-clés : Lagrange–Sylvester polynomial 
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     author = {A. A. Bobodzhanov and V. F. Safonov},
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A. A. Bobodzhanov; V. F. Safonov. “Splashes” in Fredholm Integro-Differential Equations with Rapidly Varying Kernels. Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 163-179. http://geodesic.mathdoc.fr/item/MZM_2009_85_2_a0/

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