Asymptotic behavior of the resolvent of an unstable volterra equation with kernel depending on the difference of the arguments

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. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 88–94, July, 1997. Translated by M. A. Shishkova