  In this work we obtain sufficient conditions for the existence of bounded
solutions of a resonant multi-point second-order boundary value problem, with a
fully differential equation.
  The noninvertibility of the linear part is overcome by a new perturbation
technique, which allows to obtain an existence result and a localization
theorem. Our hypotheses are clearly much less restrictive than the ones
existent in the literature and, moreover, they can be applied to higher order,
resonant or non-resonant, boundary value problems defined on the half-line or
even on the real line.
