Stability and asymptotics in nematic liquid crystals under a small Dirichlet data and a non-constant magnetic field

We consider the stability of a critical point and asymptotics of the minimizers of the free energy functional with a small Dirichlet boundary data under a non-constant exterior magnetic field in nematic liquid crystals. In the author's previous papers, we studied the stability of a critical point under the more general hypotheses but we had to assume the curl-free condition on the critical point for technical reason. However, in this paper, without the curl-free condition, we can get the similar result in the special case where the elastic coefficients are equal.