Asymptotics of solutions of Volterra integral equations with difference kernel (Q2352589)

The paper deals with the asymptotics of solutions of the Volterra integral equation with difference kernel in the case where the free term \(f\) has exponential growth as \[ f=\sum\limits^s_{l=1}e^{\mu_l t} \varphi_l(t), \, \mu_l = \alpha_l+i \beta_l, \, \alpha_l,\beta_l \in \mathbb R, \, \varphi_l \in A_m, \] where \(A_m[0,\infty)\) is the set of functions on \([0,\infty)\) and admitting the expansion \[ z(t) = \sum\limits^m_{k=0} \frac{z_k}{(t+1)^k} + \frac{o(1)}{(t+1)^m}, \, t \to \infty. \]