Bendiaf , LoubnaBenhadri , Mimia2025-01-062025-01-062024http://dspace.univ-skikda.dz:4000/handle/123456789/3703Fixed point theory has a long history of being used in nonlinear difference and differential equations, in order to prove existence, uniqueness, or other qualitative properties of solutions. However, using the fixed point theorem for the periodicity of solutions has a more recent appearance. In this disser- tation, we focus on the study of the quantitative and qualitative properties of some nonlinear delay differences and differential equations. We start by giving some fixed point theorems. After we introduce results for delay differ- ential equations and necessary relevant definitions. Finally, we derive some suffcient conditions for the existence of positive periodic solutions for the system of neutral difference equations, by using the Krasnoselskii Öxed-point theorem. An example is also given to illustrate the claims establisheenMasters degree Thesis