Positive solutions for a coupled system of non linear of second-order boundary-valued differential equations

The main objective of this article is concerned with existence and uniqueness of the positive solutions for a coupled system of second-order boundary-valued differential equations, which the boundary conditions are coupled by integrals. For that one, the solutions are related to Green’s functions and represented by integral equations and so that, we used a cone compression and expansion fixed point theorem applied to a completely continuous operator, as seen in Guo, D. and Lakshmikant V (1988).