Locally Bounded Second κ ‐Variation Solution of an Integro‐Differential Equation With Infinite Delay

This work presents conditions under which the Volterra integral equation of the second kind admits a unique solution in the class of locally bounded second κ ‐variation functions on [0, + ∞ ). Our approach relies on successive Picard iterations to obtain such a solution on a compact interval, and then to prolong it to [0, + ∞ ). We also identify criteria that guarantee the existence and uniqueness of solutions to an integro‐differential equation with infinite delay, considered within the same class of functions.