An $L^{1}$ remainder theorem for an integrodifferential equation with asymptotically periodic solution

Abstract:

For a certain integrodifferential equation of Volterra type on $(0,\infty )$, with piecewise linear convolution kernel, it is shown that the solution is $u(t) = \alpha \;\cos \beta t + \rho (t)$, with $\rho \in {L^1}(0,\infty )$ and $\alpha$ and $\beta$ constant; $u’$ is represented similarly.