Derivation of variation of parameters formulas for non- linear Volterra equations, using a method of embedding

Abstract

We show that a method of embedding for a class of non-linear Volterra equations can be used in a novel fashion to obtain variation of parameters formulas for Volterra integral equations subjected to a general type of variation of the equation. The approach is of intrinsic interest. Our variation of parameters formulas generalize classical formulas for ordinary differential equations (due to Alekseev) and for linear Volterra integral equations (based on resolvents). Illustrative examples are related to known results.