On multi-point resonant problems on the half-line

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.