Partial inverse nodal problems for differential pencils on a star-shaped graph |
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Authors: | Yu Ping Wang Chung-Tsun Shieh Xianbiao Wei |
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Institution: | 1. Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037 Jiangsu, People's Republic of China;2. Department of Mathematics, Tamkang University, Danshui Dist., New Taipei City, 25137 Taiwan (R.O.C.);3. Department of Mathematics and Physics, Anhui Jianzhu University, Hefei, 230601 People's Republic of China |
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Abstract: | 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. |
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Keywords: | inverse nodal problem differential pencil potential star-shaped graph twin-dense |
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