J. Nonl. Evol. Equ. Appl. 2023 (5), pp. 63-86, published on October 9, 2023:

On global existence results for some non-autonomous evolution systems of Volterra type in Fréchet spaces

Mamadou Moustapha Mbaye1, Amadou Diop2 and Moustapha Dieye3

1 Département de Mathématiques, Faculté des Sciences et Technique, Université Cheikh Anta Diop, BP-5005, Dakar-Fann, Sénégal
2 Laboratory of Numerical Analysis and Computer Science, Applied Mathematics Section, Gaston Berger University, Saint-Louis, Senegal.
3 Ecole Polytechnique de Thiés, Département Tronc commun, Thiés BP A10, Sénégal.

Received on April 28, 2023, revised on June 20, 2023
Accepted on June 20, 2023

Communicated by Gaston M. N'Guérékata

Abstract.  In this paper, we discuss the global existence of mild solutions for some non-autonomous deterministic and stochastic integro-differential systems with time-dependent delay in Fréchet spaces. We develop several existence results that are built on the notion of two-parameter resolvent operators in the sense of Grimmer. Examples are provided to show how the general conclusions reached in this paper are made.
Keywords: Mild solution ; Partial functional integrodifferential equations with delay ; Resolvent operator ; Nonlinear alternative of Avramescu ; C0-semigroup.
2010 Mathematics Subject Classification:   35D30 ; 45K05 ; 47H08 ; 47H10.

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