Existence Of Multiple Solutions For Some Functional Boundary Value Problems

. Let X be the Banach space of C 0 -functions on h0; 1i with the sup norm and ff; fi 2 X! R be continuous increasing functionals, ff(0) = fi(0) = 0. This paper deals with the functional differential equation (1) x 000 (t) = Q[x;x 0 ; x 00 (t)](t), where Q : X 2 \Theta R ! X is locally bounded continuous operator. Some theorems about the existence of two different solutions of (1) satisfying the functional boundary conditions ff(x) = 0 = fi(x 0 ), x 00 (1) \Gamma x 00 (0) = 0 are given. The method of proof makes use of Schauder linearizatin technique and the Schauder fixed point theorem. The results are modified for 2nd order functional differential equations. 1. Introduction There are many papers devoted to the existence of multiple solutions for ordinary and partial differential equations. We refer, for recent results on ordinary differential equations, to the papers by Chiappinelli, Mawhin and Nugari [2], Ding and Mawhin [4], Fabry, Mawhin and Nkashama [5], Gaete and..