A Variation-of-Constants Formula for Nonlinear Volterra Integral Equations of Convolution Type

摘要

With a Volterra integral equation of the convolution type, it is possible to associate a semigroup of operators acting on a space of forcing functions. Within this context, a variation-of-constants formula is derived for a certain class of nonlinear equations. It is indicated how it is possible to extend the results to other classes by considering a special equation from mathematical epidemiology.