In this article, we study the stability of black hole solutions found in the
context of dilatonic Horava-Lifshitz gravity in 1+1 dimensions by means of
the quasinormal modes approach. In order to find the corresponding quasinormal
modes, we consider the perturbations of massive and massless scalar fields
minimally coupled to gravity. In both cases, we found that the quasinormal
modes have a discrete spectrum and are completely imaginary, which leads to
damping modes. For a massive scalar field and a non-vanishing cosmological
constant, our results suggest unstable behaviour for large values of the scalar
field mass.Comment: 18 pages, 1 figure. Accepted version in EPJC. arXiv admin note: text
overlap with arXiv:gr-qc/070109
