Multiple fixed-sign solutions for a system of higher order three-point boundary-value problems with deviating arguments

We consider the following system of higher order three-point boundary-value problems ui(mi)(t)=fi(t,u1(ϕ1(t)),u2(ϕ2(t)),…,un(ϕn(t))),t∈[a,b]ui(j)(a)=0,0≤j≤mi−3ui(mi−2)(t∗)=0,ξui(mi−3)(b)+δui(mi−1)(b)=0 where i=1,2,…,ni=1,2,…,n, mi≥3mi≥3, 12(a+b)0δ>0 and ϕiϕi’s are deviating arguments. Several criteria are offered for the existence of three fixed-sign   solutions (u1,u2,…,un)(u1,u2,…,un) of the system, i.e. for each 1≤i≤n1≤i≤n and all t∈[a,b]t∈[a,b], θiui(t)≥0θiui(t)≥0 where θi∈{1,−1}θi∈{1,−1} is predetermined. We also present some examples to illustrate the results obtained.