We study the existence of positive solutions for the third order differential equation of the form
\begin{equation}\label{eqmainGS}
-u```+m^2 u`=f(t,u,u`), \quad t\in[0,1],
\end{equation}
subject to non-local boundary conditions
\begin{equation}\label{bcnonGS}
u(0)=0,\ u`(0)=\alpha[u], \ u`(1)=\beta[u],
\end{equation}
where $m>0$ and $\alpha$ and $\beta$ are the functionals (not necessarily linear) acting on the space $C^1[0,1]$.
The purpose of this poster is to present the properties of the Green`s function for the linear problem corresponding to \eqref{eqmainGS}-\eqref{bcnonGS}. The properties we focus on are used to obtain sufficient conditions implying the existence of positive and increasing solutions of the above problem.