Mathématiques

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Applications of the fixed point technique to problems generated by nonlinear functional differential equations
(university of Skikda 20 August 1955, 2023) Chouaf, Safa; Guesmia, Amar
Iterative functional di¤erential equations have a long history-more than a century, during which numerous instances have demonstrated the promising applications of these equations in multiple …elds such as medicine, biology, epidemiology, and classical electrodynamics, etc. The main aim of this dissertation is to contribute to the emerging literature of this type of equations via the study of three classes of second order iterative functional di¤erential equations in Banach spaces. We establish some existence and uniqueness results and the continuous dependence on parameters of the unique solution by virtue of a powerful technique that combines the …xed point theory and the Green’s function method. More precisely, it is based on the transformation of the considered problem into a …xed point problem by converting it into an equivalent integral equation whose kernel is a Green’s function before applying the Banach and Schauder …xed point theorems