In this thesis, we study modelling with non-linear ordinary di erential equa-tions, and the existence of positive solutions for Boundary Value Problems (BVPs).These problems have wide applications in many areas. The focus is on the extensionsof previous work done on non-linear second-order di erential equations with bound-ary conditions involving rst-order derivative. The contribution of this thesis hasfour folds. First, using a xed point theorem on order intervals, the existence of apositive solution on an interval for a non-local boundary value problem is obtained.Second, considering a di erent boundary value problem that consists of the rst-orderderivative in the non-linear term, an increasing solution is obtained by applying theKrasnoselskii-Guo xed point theorem. Third, the existence of two solutions, onesolution and no solution for a BVP is proved by using xed point index and iterationmethods. Last, the results of Green's function unify some methods in studying theexistence of positive solutions for BVPs of nonlinear di erential equations. Examplesare presented to illustrate the applications of our results.Keywords:Boundary Value Problems, Positive Solutions, Di erential Equa-tions, Fixed Point, Banach Space, Norm, Operator.