  We study stability of singularity-free cosmological solutions with positive
cosmological constant based on projectable Ho\v{r}ava-Lifshitz (HL) theory. In
HL theory, the isotropic and homogeneous cosmological solutions with bounce can
be realized if spacial curvature is non-zero. By performing perturbation
analysis around non-flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime,
we derive a quadratic action and discuss the stability, i.e, ghost and
tachyon-free conditions. Although the squared effective mass of scalar
perturbation must be negative in infrared regime, we can avoid tachyon
instability by considering strong Hubble friction. Additionally, we estimate
the backreaction from the perturbations on background geometry, especially,
against anisotropic perturbation in closed FLRW spacetime. It turns out that
certain types of bouncing solution may be spoiled even if all perturbation
modes are stable.
