The Green function of the boundary value problem on a star-shaped graph
The author considers a planar graph consisting of three edges with one common vertex. He is interested in the sign of the Green function of the boundary value problem for a fourth-order equation. This problem models deformations of star-shaped coupled networks of beams. The author assumes that the network is fixed at each vertex, and all beams are rigidly jointed at their common vertex. He proves that the Green function is positive on diagonal squares and establishes a sufficient condition for its positivity inside its domain of definition.
scientific article; zbMATH DE number 6152679