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Inverse spectral problems for differential pencils with boundary conditions dependent on the spectral parameter
Author(s) -
Wang Yu Ping,
Yurko V.A.
Publication year - 2016
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.4235
Subject(s) - mathematics , eigenvalues and eigenvectors , inverse , boundary value problem , type (biology) , mathematical analysis , differential (mechanical device) , differential equation , spectral properties , boundary (topology) , inverse problem , pure mathematics , geometry , ecology , chemistry , physics , computational chemistry , quantum mechanics , engineering , biology , aerospace engineering
In this paper, we discuss two inverse problems for differential pencils with boundary conditions dependent on the spectral parameter. We will prove the Hochstadt–Lieberman type theorem of [Disp. Item 1. lu:=−u′′+[q(x)+2ρp(x)]u=ρ2u,x∈(0,π) ...]–[Disp. Item 3. V(u):=u′(π,ρ)+(H1ρ+H0)u(π,ρ)=0, ...] except for arbitrary one eigenvalue and the Borg type theorem of [Disp. Item 1. lu:=−u′′+[q(x)+2ρp(x)]u=ρ2u,x∈(0,π) ...]–[Disp. Item 3. V(u):=u′(π,ρ)+(H1ρ+H0)u(π,ρ)=0, ...] except for at most arbitrary two eigenvalues, respectively. The new results are generalizations of the related results. Copyright © 2016 John Wiley & Sons, Ltd.