Existence Results of Mild Solutions for Second Order Perturbed Pseudo Integro-Differential Evolution Equations with Infinite State-Dependent delay in Fréchet Spaces

Imane Abibssi; Selma Baghli-Bendimerad

doi:10.2478/tmmp-2025-0023

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Existence Results of Mild Solutions for Second Order Perturbed Pseudo Integro-Differential Evolution Equations with Infinite State-Dependent delay in Fréchet Spaces

Tatra Mountains Mathematical Publications

Volume 90 (2025): Issue 2 (December 2025)

By: Imane Abibssi and Selma Baghli-Bendimerad

Open Access

|Dec 2025

Abstract

This paper is concerned with the existence of mild solutions in Fréchet spaces combined with semigroup theory, using Avramescu’s nonlinear alternative for the sum of compact operators and contraction maps, to the second order perturbed pseudo integro-differential evolution equations with state-dependent delay.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2025-0023 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 51 - 78

Submitted on: Jun 5, 2023

Accepted on: Sep 19, 2025

Published on: Dec 18, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

perturbed pseudo integro-differential evolution equations,

second order,

neutral problems,

mild solutions,

state-dependent delay,

fixed point,

nonlinear alternative,

Related subjects:

© 2025 Imane Abibssi, Selma Baghli-Bendimerad, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 90 (2025): Issue 2 (December 2025)