Résumé:
The aim of this work is to study and to prove the uniqueness and the positivity of a nontrivial solution for a boundary problem generated by a second order differential equation, we used Banach's contraction principle and the Guo-Krasnosel'skii fixed point theorem. This work contains an introduction and three chapters. In the first, we discuss the fundamental concepts of functional analysis that we will use in the following. In the second, we present essential theoretical results on the fixed point theory and some important theorems. The third chapter is based on the study of the uniqueness and positivity of the solution of a three point boundary value problem of second order, we used the Banach contraction principle and the Guo-Krasnosel'skii fixed point theorem. The results obtained are illustrated by examples. We finalize this thesis by a bibliography
