Existence and nonexistence of positive solutions for second-order time scale systems

This paper is concerned with the following system on time scale TT: {uiΔΔ(t)+fi(u1(t),u2(t),…,un(t))=0,t∈[0,T]T,uiΔ(0)=0=ui(σ2(T)),i=1,2,…,n, where 0,T∈T0,T∈T and T>0T>0. By using the theory of the fixed point index, we investigate the effect of σ2(T)σ2(T) on the existence and nonexistence of positive solution for the above system in sublinear cases. The results obtained are even new for the special cases of difference system and differential system, as well as in the general time scale setting.