In this article, we deal with the existence of solutions for the following second-order differential equation: � u′′(t) = f(t, u(t)) + h(t) u(a) − u(b) = u′(a) − u′(b) = 0, where B is a reflexive real Banach space, f : [a, b] × B → B is a se- quentially weak-strong continuous mapping, and h : [a, b] → B is a continuous function on B. The proofs are obtained using a recent gen- eralization of the well-known Bolzano-Poincar´e-Miranda theorem to infinite-dimensional Banach spaces. In the last section, we present three examples of application of the general result.
