A model of string system deformations on a star graph with nonlinear condition at the node

In this paper, a model of deformations of Stieltjes strings system located along a geometric star graph with a nonlinear condition at the node is studied. This kind of condition arises due to the presence of a limiter for the movement of strings in the node under the influence of an external load. In the present paper, the necessary and sufficient conditions for the extremum of the energy functional are established; existence and uniqueness theorems for the solution are proved; the critical loads at which the strings come into contact with the limiter are analyzed; the dependence of the solution on the limiter length is studied.