This paper presents sufficient conditions for the solvability of the third
order three point boundary value problem \begin{equation*} \left\{
\begin{array}{c} -u^{\prime \prime \prime }(t)=f(t,\,v(t),\,v^{\prime }(t)) \\
-v^{\prime \prime \prime }(t)=h(t,\,u(t),\,u^{\prime }(t)) \\ u(0)=u^{\prime
}(0)=0,u^{\prime }(1)=\alpha u^{\prime }(\eta ) \\ v(0)=v^{\prime
}(0)=0,v^{\prime }(1)=\alpha v^{\prime }(\eta ).
\end{array}
\right. \end{equation*} The arguments apply Green's function associated to
the linear problem and the Guo--Krasnosel'ski\u{\i} theorem of
compression-expansion cones. The dependence on the first derivatives is
overcome by the construction of an adequate cone and suitable conditions of
superlinearity/sublinearity near 0 and +∞. Last section contains an
example to illustrate the applicability of the theorem.Comment: 21 page
