Existence and multiplicity of solutions for functional boundary value problems

The system of second order functional differential equations (x(')(t) + L(x('))(t))' = F(x)(t) is considered. Here L : C-0(J;R-n) --> C-0(J;R-n) and F : C-1(J;R-n) --> L-1(J;R-n) are continuous operators. Sufficient conditions for the existence of at least 2(n) solutions of the above system satisfying the functional boundary conditions alpha (i)(x(i)) = A(i), max {x(i)(t) : t is an element of J} - min{x(i)(t) : t is an element of J} = B-i (i = 1,..., n) are given'. Here alpha (i) : C-0(J; R) --> R are continuous increasing functionals. and x = (x(1),...,x(n)). Existence results are proved by the topological degree method for alpha -condensing operators.