Mild Solutions for Nonlocal Second Order Partial Functional and Neutral Functional Perturbed Evolution Equations with Infinite State-Dependent Delay

Document Type : Original Article

Authors

Imane Abibssi ¹

Zohra Bouteffal ²

Selma Baghli-Bendimerad ³

¹ Laboratory of Mathematics‎, ‎Djillali Liabes University of Sidi Bel Abbes‎, ‎P‎. ‎O‎. ‎Box 89 Sidi bel Abbes 22000‎, ‎Algeri

² Ecole Superieure en Informatique‎, ‎Sidi Bel-Abb\`es 22000‎, ‎Algerie

³ Exact Sciences Faculty‎, ‎Department of Mathematics‎, ‎Djillali Liabes University of Sidi Bel Abbes‎, ‎P‎. ‎O‎. ‎Box 89 Sidi bel Abbes 22000, Algeria

10.22034/kjm.2025.476176.3312

Abstract

This paper focuses on establishing the existence of mild solutions over a semi-infinite interval for two types of second-order perturbed evolution equations that involve infinite statedependent delays under nonlocal conditions. The approach employs Avramescu’s nonlinear alternative for the sum of compact operators and contraction mappings in Fréchet spaces, alongside semigroup theory.

Keywords

Nonlinear alternative

semigroup theory

Fréchet spaces

infinite delay

Subjects

• 34 Ordinary differential equations

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