Ambrosetti–Prodi periodic problem of Minkowski-curvature equations with an indefinite repulsive singularity

The existence, nonexistence, and multiplicity of positive [Formula: see text]-periodic solutions to a class of Minkowski-curvature equations with an indefinite repulsive singularity are investigated in the paper. An Ambrosetti–Prodi type result is established using a continuation theorem of coincidence degree and certain properties of Leray–Schauder degree. Further, we provide a dynamic behavior of positive [Formula: see text]-periodic solutions with respect to parameter [Formula: see text].