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

Author

Listed:
  • Luz Elimar Marchan
  • Luis Fernando Mejías
  • Liliana Pérez

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.

Suggested Citation

  • Luz Elimar Marchan & Luis Fernando Mejías & Liliana Pérez, 2026. "Locally Bounded Second κ-Variation Solution of an Integro-Differential Equation With Infinite Delay," International Journal of Differential Equations, Hindawi, vol. 2026, pages 1-8, April.
    • Handle: RePEc:hin:jnijde:3097411
    DOI: 10.1155/ijde/3097411
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