A boundary value problem for functional differential equations of delay type (Q1080040)

The authors develop a series of existence and uniqueness conditions for solutions of the nonhomogeneous boundary value problem of the nonlinear functional differential equation \[ x'(t)=L(t,x_ t)+f(t,x_ t),\quad a\leq t\leq b,\quad Mx_ a+Nx_ b=\emptyset. \] These results are extensions of the results of \textit{R. Fennel} and \textit{P. Waltman} [ibid. 26, 447-453 (1969; Zbl 0172.121)] and \textit{P. Waltman} and \textit{J. Wong} [Trans. Am. Math. Soc. 164, 39-54 (1972; Zbl 0263.34072)] to a larger class of perturbations and are developed through the concept of local spectrum and the method of shooting. The paper concludes with several extensive examples of these results.