Multiple fixed-sign solutions for a system of generalized right focal problems with deviating arguments

We consider the following system of generalized right focal boundary value problemsui‴(t)=fi(t,u1(ϕ1(t)),u2(ϕ2(t)),…,un(ϕn(t))),t∈[a,b],ui(a)=ui′(t∗)=0,ξui(b)+δui″(b)=0,1⩽i⩽n, where 12(a+b)0δ>0 and ϕiϕi, 1⩽i⩽n1⩽i⩽n are deviating arguments. By using different fixed point theorems, we develop several criteria for the existence of three solutions of the system which are of fixed sign   on the interval [a,b][a,b], i.e., for each 1⩽i⩽n1⩽i⩽n, θiui(t)⩾0θiui(t)⩾0 for all t∈[a,b]t∈[a,b] and fixed θi∈{1,−1}θi∈{1,−1}. Examples are also included to illustrate the results obtained.