Electrostatic perturbations propagating obliquely to the magnetic field lines are studied in a cylindric magnetized dusty plasma configuration. A set of two coupled equations describing the perturbed electrostatic and gravity potentials in a radially nonuniform plasma is derived. The equations are discussed and solved in two limits, without and with the self-gravity effects included. Without the gravity the corresponding equation for the electrostatic potential is solved analytically for a Gaussian-type equilibrium density profile. The general solution, which can be applied to various plasma situations, is expressed in terms of the Kummer confluent hypergeometric functions. In the self-gravitating case the equations are solved analytically for a homogeneous plasma and the general solutions are written in terms of the Bessel functions, describing well-behaving radially localized wave amplitudes. (C) 2004 American Institute of Physics.