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

Luz Elimar Marchan, Luis Fernando Mejías and Liliana Pérez

International Journal of Differential Equations, 2026, vol. 2026, 1-8

Abstract: 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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:3097411

DOI: 10.1155/ijde/3097411

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