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A non‐standard multiparameter eigenvalue problem in ordinary differential equations
Author(s) -
Faierman M.,
Mennicken R.
Publication year - 2005
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.200410321
Subject(s) - eigenfunction , mathematics , eigenvalues and eigenvectors , ordinary differential equation , mathematical analysis , differential operator , oscillation theory , oscillation (cell signaling) , principal (computer security) , differential equation , differential algebraic equation , computer science , physics , quantum mechanics , biology , genetics , operating system
We consider two simultaneous Sturm–Liouville systems involving three spectral parameters. However unlike the standard multiparameter problem, we now suppose that the principal part of each of the differential operators involved is multiplied by a different parameter. For such a non‐standard system we establish the oscillation theory and discuss the associated eigenfunction expansion. Some open problems concerning the eigenfunction expansion are also presented. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)