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In this paper we obtain the explicit expression of the Green's functionrelated to a general $n$ order differential equation coupled to non-locallinear boundary conditions. In such boundary conditions, a $n$ dimensionalparameter dependence is also assumed. Moreover, some comparison principles areobtained.  The explicit expression depends on the value of the Green's function relatedto the two-point homogeneous problem, that is, we are assuming that when allthe parameters involved on the boundary conditions take the value zero then theproblem has a unique solution which is characterized by the correspondingGreen's function $g$. The expression of the Green's function $G$ of the generalproblem is given as a function of $g$ and the real parameters considered at theboundary conditions.  It is important to show that, in order to ensure the uniqueness of solutionsof the linear considered problem, we must assume a non resonant additionalcondition on the considered problem, which depends on the non local conditionsand the corresponding parameters.  We point out that the assumption of the uniqueness of solutions of thetwo-point homogeneous problem is not a necessary condition to ensure thesolution of the general case. Of course, in this situation the expression weare looking for must be obtained in a different manner.  To show the applicability of the obtained results, a particular example isgiven.

Green's function related to a n order linear differential equation coupled to arbitrary linear non local boundary conditions