Abstract
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: x''(t) = f(t,x,x'(t)), t \\in [0,T], \\alpha_0 x_0 - \\alpha_1 x'(0) = \\varphi \\in C_r \\beta_0 x(T) + \\beta_1 x'(T) = A \\in {\\Bbb R}^n. 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.
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