Boundary Value Problems for Functional Differential Equations

This paper is concerned with the existence of solutions of a boundary value problem for second-order functional differential equations. Specifically the following problem is considered: x0 t.sf t, xt, x9 t.., tgw0, Tx, a0x0ya1x9 0.swgCr b0x T.qb1x9 T.sAgRn. The results are based on a nonlinear alternative of Granas and the use of a priori bounds on solutions. Some examples are also discussed to illustrate how these results may be used to yield the existence of solutions of specific boundary value problems.