Applications of the fixed point technique to problems generated by nonlinear functional differential equations
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Date
2023
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Publisher
university of Skikda 20 August 1955
Abstract
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