Mathématiques

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Existence results for certain delay differential equations
(université 20aout 1955 skikda, 2024) Marwa, KHEMIS; Ahlème,BOUAKKAZ
The objective of this thesis is to study the existence, uniqueness and stability of positive, periodic and bounded solutions for four …rst order delay di¤erential equations with iterative terms. For achieving our target, we convert each problem into an equivalent integral equation whose kernel is a Green’s function, and then we apply the Krasnoselskii or Schauder …xed point theorems with the help of some properties of the obtained kernel and some functional analysis tools in order to establish the existence results. Whereas the uniqueness and continuous dependence results are obtained by using the Banach contraction mapping principle. In addition, many illustrative examples are exhibited to demonstrate the validity of our theoretical …ndings which are novel and complement some existing results in the literature.