Abstract :
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
