Abstract :
We consider the discrete system
Δmui(k) = Pi k,u1(k),u2(k), . . . , un(k) , k∈ {0, 1, . . . , N}, 1 i n,
together with Hermite boundary conditions,
Δj ui(kν ) = 0, j= 0, . . . , mν − 1, ν = 1, . . . , r, 1 i n,
where r 2, mν 1 for ν = 1, . . . , r, r
ν=1mν = m, and kν’s are integers such that 0 = k1 <
k1 + m1 < k2 < k2 + m2 < ··· < kr kr + mr − 1 = N + m. By using the Leggett–Williams
fixed point theorem and the Five functionals fixed point theorem, we establish two different sets of
criteria for the existence of three solutions of the system which are of ‘fixed-signs.’ Examples are
also included to illustrate the results obtained.
2004 Elsevier Inc. All rights reserved.
