The Green function of the boundary value problem on a star-shaped graph. (English. Russian original) Zbl 1279.34045
Russ. Math. 57, No. 2, 48-57 (2013); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2013, No. 2, 56-66 (2013).
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.
Reviewer: Chuan-Fu Yang (Nanjing)
MSC:
| 34B45 | Boundary value problems on graphs and networks for ordinary differential equations |
| 34B27 | Green’s functions for ordinary differential equations |
References:
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