Solutions of constant signs of a system of Sturm-Liouville boundary value problems

We consider the following system ui(m)(t) + ƒi(t, u1(t), u2(t),…un(t))= 0, t ϵ[0, 1], uij(0) = 0, 0 ≤j ≤m− 3, αiui(m−2)(0)- βiui(m−1)(0) = 0, γiui(m−2)(1) + δiui(m−1)δiui(m−1) = 0, i = 1,2,…,n, where m ≥ 2 and for each 1≤ i ≤ n, βi≥ 0, δi≥ 0,βi+αi> 0, δi+γi > 0, and αiγi +αiδi+βiγi> 0. Criteria are offered for the existence of single and twin solutions of the system that are of constant signs.