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The objective of the book is devoted to the study of the existence of solutions for some boundary value problem generated by the fourth and fifth order nonlinear differential equations. In the first three results, we establish the existence of positives solutions for nonlinear fifth-order differential equations with two and three points boundary conditions by using some fixed points theorems notably, the Schauder-theorem, Guo-Krasnosel'skii theorem on expansion and compression of cones and the upper and lower technical solutions. In the fourth chapter, we establish the existence of multiple positive solutions for a system of nonlinear second-order three point boundary value problem by using the Leggett-Williams fixed point theorem.In the last chapter, we are interested the existence of solutions and multiple solutions for differential fourth-order differential equation with deviating arguments by using the Schauder fixed point theorems, the concept of the topological degree and the method of upper and lower solutions.