Three fixed-sign solutions of system model with Sturm–Liouville type conditions

We consider the following system of differential equations u (mi ) i (t )+ Pi t,u1(t ),u2(t ), . . . ,un(t ) = 0, t∈ [0, 1], 1 i n together with Sturm–Liouville boundary conditions u (j ) i (0) = 0, 0 j mi − 3, ξu (mi−2) i (0) − ηu (mi−1) i (0) = 0, ωu (mi−2) i (1) + δu (mi−1) i (1) = 0, 1 i n, where mi 2 for each 1 i n, η 0, δ 0, η +ξ >0, δ +ω >0, and ξω + ξδ + ηω > 0. By using two different fixed point theorems, we offer criteria for the existence of three solutions of the system which are of fixed signs on the interval [0, 1]. Examples are also included to illustrate the results obtained.  2004 Elsevier Inc. All rights reserved