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Determination of differential pencils with spectral parameter dependent boundary conditions from interior spectral data
Author(s) -
Yang ChuanFu,
Yu XiuJuan
Publication year - 2014
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.2844
Subject(s) - mathematics , eigenfunction , interval (graph theory) , mathematical analysis , boundary value problem , differential equation , spectrum (functional analysis) , differential (mechanical device) , point (geometry) , boundary (topology) , eigenvalues and eigenvectors , combinatorics , geometry , physics , quantum mechanics , thermodynamics
Second‐order differential pencils L ( p , q , h 0 , h 1 , H 0 , H 1 ) on a finite interval with spectral parameter dependent boundary conditions are considered. We prove the following: (i) a set of values of eigenfunctions at the mid‐point of the interval [0, π ] and one full spectrum suffice to determine differential pencils L ( p , q , h 0 , h 1 , H 0 , H 1 ); and (ii) some information on eigenfunctions at some an internal point b ∈ (π 2 , π ) and parts of two spectra suffice to determine differential pencils L ( p , q , h 0 , h 1 , H 0 , H 1 ). Copyright © 2013 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.
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