Degenerate/singular beam-type equations: A controllability result

The paper deals with the controllability of a degenerate/singular beam-type equation in divergence or non-divergence forms. In particular, we assume that the degeneracy and singularity are at the same boundary point, and we consider a suitable control $ f $ localized on the non-degenerate boundary point. As a first step, we prove the existence of a solution for the homogeneous problems, then we prove some estimates on their energies. Based on them, we prove two observability inequalities and, using the notion of solution by transposition, we prove that the initial problems are null controllable.