On some variation of parameter methods for integrodifferential, integral, and quasilinear partial integrodifferential equations

摘要

A nonlinear variation of parameter method of Bernfeld and Lord for systems of ordinary integrodifferential and integral equations is corrected and extended. Representation formulas for certain solutions of perturbations of such systems are obtained. A correction and extension of a similar recent result of Pachpatte for a quasilinear partial integrodifferential equation is also given. Some applications are given to stability and boundedness properties of solutions of systems of integrodifferential and integral equations.