  In the present article, Radiative Correction (RC) to the Casimir energy was
computed for the self-interacting massive/massless Lifshitz-like scalar field,
confined between a pair of plates with Dirichlet and Mixed boundary conditions
in $3+1$ dimensions. Moreover, using the results obtained for the Dirichlet
Casimir energy, the RC to the Casimir energy for Periodic and Neumann boundary
conditions were also draw outed. To renormalize the bare parameters of the
Lagrangian, a systematic perturbation expansion was used in which the
counterterms were automatically obtained in a position-dependent manner. In our
view, the position dependency of the counterterm was allowed, since it
reflected the effects of the boundary condition imposed or the background space
in the problem. All the answers obtained for the Casimir energy were consistent
with well-known physical expects. In the language of graphs, the Casimir energy
for the massive Lifshitz-like scalar field confined with four boundary
conditions (Dirichlet, Neumann, Mixed, and Periodic) was also compared to each
other, and as a concluding remark, the sign and magnitude of their values were
discussed.
