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Determination of differential pencils from dense nodal subset in an interior subinterval

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Abstract

The uniqueness problem of the inverse nodal problem for the differential pencils defined on interval [0, 1] with the Dirichlet boundary conditions is considered. We prove that a bilaterally dense subset of the nodal set in interior subinterval (a 1, a 2)(⊂ [0, 1]) can determine the pencil uniquely. However, in the case of 1/2 ∉ [a 1, a 2] we need additional spectral information to treat this problem, which is associated with the derivatives of eigenfunctions at some known nodal points.

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  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, PR China

    Yongxia Guo & Guangsheng Wei

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  1. Yongxia Guo
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  2. Guangsheng Wei
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Correspondence to Guangsheng Wei.

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Guo, Y., Wei, G. Determination of differential pencils from dense nodal subset in an interior subinterval. Isr. J. Math. 206, 213–231 (2015). https://doi.org/10.1007/s11856-014-1139-3

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  • DOI: https://doi.org/10.1007/s11856-014-1139-3

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