Geodesic
Asymptotic behavior of the resolvent of an unstable Volterra equation with kernel depending on the difference of the arguments
Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 88-94

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We present the structure of the resolvent of a difference kernel, which allows us to study the asymptotic behavior of the solution of the renewal equation for a given asymptotic behavior of the constant term. An asymptotic representation for the resolvent is obtained under minimal requirements on the moments of the kernel. Similar results are given for integro-differential equations. 
@article{MZM_1997_62_1_a8,
     author = {V. A. Derbenev and Z. B. Tsalyuk},
     title = {Asymptotic behavior of the resolvent of an unstable {Volterra} equation with kernel depending on the difference of the arguments},
     journal = {Matemati\v{c}eskie zametki},
     pages = {88--94},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a8/}
}
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V. A. Derbenev; Z. B. Tsalyuk. Asymptotic behavior of the resolvent of an unstable Volterra equation with kernel depending on the difference of the arguments. Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 88-94. http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a8/