Mebaoudj ,RayaneBenhadri ,Mimia2025-11-252025-11-252025http://dspace.univ-skikda.dz:4000/handle/123456789/5491The aimofthisworkistostudytheexistenceofperiodicsolutionsforanonlinearsystem of neutraldifferentialequationswithvariabledelays. In theprocess,wetransformthedifferentialsystemintoanequivalentintegralsystem. Then, weconstructappropriatemappingsonaboundedclosedandconvexsetofaBanach space. Underspecificconditions,weapply the Krasnoselskiifixedpointtheorem for obtaining the existenceresult.Whereas,theexistenceofauniqueperiodicsolutionisdeterminedby the contractionmappingprinciple. Ourresultsareconsideredageneralizationofsomecon- clusions proposedinrecentliterature.Themainresultsareillustratedwithanappropriate exampleenExistence of periodic solutions for a nonlinear system of neutral differential equationsA. F. A.Thesis