Symmetric solutions of a multi-point boundary value problem

We apply the fixed point theorem of Avery and Peterson to the nonlinear second-order multi-point boundary value problem −u (t) = a(t)f t,u(t), u (t) , t∈ (0, 1), u(0) = n i=1 μiu(ξi ), u(1−t) = u(t), t ∈ [0, 1], where 0 < ξ1 < ξ2 < ··· < ξn 12 , μi > 0 for i = 1, . . . , n with n i=1 μi < 1, n 2. We show that under the appropriate growth conditions on the inhomogeneous term symmetric about t = 12 the problem has triple symmetric solutions.  2004 Elsevier Inc. All rights reserved