What question did this study set out to answer?

To establish conditions for unique solutions within locally bounded second κ-variation functions for integro-differential equations with infinite delay.

May 6, 2026Open Access

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

Key Points

To establish conditions for unique solutions within locally bounded second κ-variation functions for integro-differential equations with infinite delay.
Analyzed Volterra integral equations of the second kind.
Utilized Picard iterations for solution attainment.
Extended solutions from compact intervals to [0, + ∞ ).
Demonstrated existence and uniqueness of solutions for the integro-differential equation.
Identified specific criteria for solution validity within the second κ-variation function class.

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.

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Authors

Luz Elimar Marchan

Luis Fernando Mejías

Liliana Pérez

Journals

International Journal of Differential Equations

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

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Authors

Journals

Actions

References and Citations

Citation Network

Connected Papers

Discussion

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