Partial inverse nodal problems for differential pencils on a star‐shaped graph

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 o...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-10, Vol.43 (15), p.8841-8855
Main Authors: Wang, Yu Ping, Shieh, Chung‐Tsun, Wei, Xianbiao
Format: Article
Language:English
Subjects:
differential pencil
Entire functions
Intervals
inverse nodal problem
Pencils
potential
star‐shaped graph
twin‐dense
Uniqueness theorems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6574