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On solvability of three spectra problem
Author(s) -
Boyko Olga,
Pivovarchik Vyacheslav,
Yang Chuan Fu
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400382
Subject(s) - mathematics , dirichlet distribution , dirichlet eigenvalue , boundary value problem , dirichlet's principle , elliptic boundary value problem , dirichlet boundary condition , neumann boundary condition , dirichlet problem , mathematical analysis , mixed boundary condition
Three spectral problems generated by the same Sturm–Liouville equation are considered: Neumann–Dirichlet problem (the Neumann condition at the left end and the Dirichlet condition at the right end) on the whole interval [0, a ], Neumann–Dirichlet problem on [ 0 , a / 2 ] and Dirichlet–Dirichlet problem on [ a / 2 , a ] . The three spectra inverse problem, i.e. the problem of recovering the Sturm–Liuville equation using the three spectra of these boundary value problems is completely solved.