Mathématiques

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Fixed point technique and its applications to functional differential equations with delay
(20 Août 1955 university of Skikda, 2025) Elbahi, Amel; Benhadri , Mimia
For long time …xed point theory has been used extensively in nonlinear di¤erential equations to investigate the properties of solutions both quantitatively and qualitatively. One of the most signi…cant qualitative features of di¤erential equations is the determination of their periodicity. The main objective of this thesis is to investigate the existence of bounded positive periodic solutions for a class of …rst-order nonlinear neutral di¤erential equations with iterative terms and impulsive e¤ects. In the process, we convert the given equation into an equivalent integral equation. Then, we construct a suitable mapping and use a hybrid technique that combines Shauder’s …xed point approach, Green’s functions method, and some functional analysis tools to achieve our purpose. Easily veri…able su¢ cient conditions are established. The equation considered is more general and incorporates as special cases various problems widely studied in di¤erent literature. In our applications, two examples are analyzed to demonstrate the real power of our results.