The structure of the plasma-wall boundary around a negatively biased spherical electrode immersed in low-pressured electronegative plasma was studied numerically using a fluid model as well as a particle-in-cell Monte Carlo (PIC-MC) simulation. The range of plasma parameters, such as negative-ion/electron density ratio and electron/ion temperature ratios, in which the boundary region involves both positive and negative space charges, is derived using the fluid model with warm positive ions and with and without positive-ion collisionality. Contrary to the recent results for planar discharge (Franklin R N and Snell J 2000 J. Phys. D: Appl. Phys. 33 1990), with the cold-positive-ion assumption relaxed, the fluid model does predict a complex sheath structure with non-monotonic potential, even for positive-ion temperatures as high as the electron temperature if the negative ion temperature is sufficiently low. A comparison between the fluid model and PIC-MC simulation was made for a case where the fluid model predicts potential oscillations. In the collisionless limit, the PIC-MC results were almost identical with the fluid-model results. However, with weak collisionality included, the results from the two approaches differed drastically. While the fluid-model prediction remained essentially unchanged, the PIC-MC simulation showed a temporally oscillating non-monotonic potential, the oscillation apparently periodically releasing the ions trapped in the potential well. This indicates that when the fluid model predicts spatial potential oscillation, instability can be induced in the real physical potential.