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Partial inverse nodal problems for differential pencils on a star‐shaped graph
Author(s) -
Wang Yu Ping,
Shieh ChungTsun,
Wei Xianbiao
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6574
Subject(s) - mathematics , star (game theory) , inverse problem , nodal , uniqueness , modified nodal analysis , vertex (graph theory) , graph , inverse , partial differential equation , cardinal point , pure mathematics , combinatorics , mathematical analysis , geometry , medicine , anatomy , physics , optics
In this paper, the authors study partial inverse nodal problems for differential pencils on a star‐shaped graph. We firstly show that the potential on each edge can be uniquely determined by twin‐dense nodal subsets on some interior intervals under certain conditions. Without any nodal information on some potential on the fixed edge, we may add some spectral information to guarantee these uniqueness theorems. We still consider the case of arbitrary intervals having the internal vertex. In particular, we pose and solve a new partial inverse nodal problem for differential pencils on the star‐shaped graph from the Weyl m ‐function and the theory concerning densities of zeros of entire functions.