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 problems u i ‴ ( t ) = f i ( t , u 1 ( ϕ 1 ( t ) ) , u 2 ( ϕ 2 ( t ) ) , … , u n ( ϕ n ( t ) ) ) , t ∈ [ a , b ] , u i ( a ) = u i ′ ( t ∗ ) = 0 , ξ u i ( b ) + δ u i ″ ( b ) = 0 , 1 ⩽ i ⩽ n , where 1 2 ( a + b ) t ∗ b , ξ ⩾ 0 , δ > 0 and ϕ i , 1 ⩽ 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 ] , i.e., for each 1 ⩽ i ⩽ n , θ i u i ( t ) ⩾ 0 for all t ∈ [ a , b ] and fixed θ i ∈ { 1 , − 1 } . Examples are also included to illustrate the results obtained.