The stability of Fermat – Torricelli problem's locus in normed planes

The article studies the structure of non-unique solutions of the Fermat–Torricelli problem in normed planes. The problem of the presence of the stability property for such solutions was posed. The results were obtained in the form of necessary and sufficient conditions for the stability of all solutions for sets of three points in a normed plane. In addition, as an illustration, bifurcation diagrams of solutions were considered and their structure was investigated.