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We study $k$-radially symmetric solutions corresponding to topologicaldefects of charge $\frac{k}{2}$ for integer $k \neq 0$ in the Landau-de Gennesmodel describing liquid crystals in two-dimensional domains. We show that thesolutions whose radial profiles satisfy a natural sign invariance are stablewhen $|k| = 1$ (unlike the case $|k|>1$ which we treated before). The proofcrucially uses the monotonicity of the suitable components, obtained by makinguse of the cooperative character of the system. A uniqueness result for theradial profiles is also established.

Stability of point defects of degree $\pm \frac 1 2$ in a two-dimensional nematic liquid crystal model