We study within a mean-field approach the stationary states of the kinetic spin-1 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field. We use the Galuber-type stochastic dynamics to describe the time evolution of the system. We have found that the behavior of the system strongly depends on the crystal field interaction D. We have obtained two types of solutions: a symmetric one, which corresponds paramagnetic phase where the magnetization (m) of the system oscillates in time around zero, and an antisymmetric one where m oscillates in time around a finite value different from zero. There are regions of the phase space where both solutions coexist. The dynamic phase transition from one regime to the other can be a first- or a second-order depending on the region in the phase diagram. Hence, the system exhibits one or more dynamic tricritical point, which depends on the values D. We also calculate the Liapunov exponent to verify the stability of the solutions and the dynamic phase transition points. © 2005 The American Physical Society.