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) = fi t,u1 φ1(t) ,u2 φ2(t) , . . . , un φn(t) , t∈ [a, b], ui(a) = u i (t∗) = 0, ξui (b) +δu i (b) = 0, 1 i n, where 12 (a + b) < t∗ 0 and φi, 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, θiui (t) 0 for all t ∈ [a, b] and fixed θi ∈ {1,−1}. Examples are also included to illustrate the results obtained. © 2005 Elsevier Inc. All rights reserved