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 is an element of (0, 1), u(0)= Sigma(i=1)mu iu(zeta i), u(1-t)=u(t), t is an element of[0,1], where 0 <zeta(1) < zeta(2) < ...< zeta(11) <= 1/2, mu > 0 for i = 1, ... , n with Sigma(n)(i=1) < 1, n >= 2.We show that under the appropriate growth conditions on the inhomogeneous term symmetric about t = 1/2 the problem has triple symmetric solutions. (c) 2004 Elsevier Inc. All rights reserved.