Ambrosetti–Prodi type multiplicity result for a wave equation with sublinear nonlinearity

We shall prove a weakened Ambrosetti–Prodi type multiplicity result for a wave equation with sublinear nonlinearity and without damping. Due to infinite-dimensional kernel of the wave operator, the Leray–Schauder and coincidence degrees are not available. We use an extension of the Leray–Schauder degree to obtain multiple solutions.