Geodesic
``Splashes'' in Fredholm Integro-Differential Equations with Rapidly Varying Kernels
Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 163-179

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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 
@article{MZM_2009_85_2_a0,
     author = {A. A. Bobodzhanov and V. F. Safonov},
     title = {``Splashes'' in {Fredholm} {Integro-Differential} {Equations} with {Rapidly} {Varying} {Kernels}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--179},
     publisher = {mathdoc},
     volume = {85},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_2_a0/}
}
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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/