Stability of Volterra equations

Summary

Stability of a Volterra integral equation concerns the behaviour of its solutions on the whole half-line $t \ge 0$. For a linear equation of convolution type it asks whether bounded or integrable data always give bounded or integrable solutions. This holds when the resolvent kernel of the equation is integrable, which is the standard notion of stability for such equations. Stability results are used for models with memory, such as viscoelastic materials, feedback systems with delay and population dynamics.