The interlacing of eigenvalues for periodic multi-parameter problems
1978 ◽
Vol 80
(3-4)
◽
pp. 357-362
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Keyword(s):
SynopsisThis paper studies a linked system of second order ordinary differential equationswhere xx ∈ [ar, br] and the coefficients qrars are continuous, real valued and periodic of period (br − ar), 1 ≤ r,s ≤ k. We assume the definiteness condition det{ars(xr)} > 0 and 2k possible multiparameter eigenvalue problems are then formulated according as periodic or semi-periodic boundary conditions are imposed on each of the equations of (*). The main result describes the interlacing of the 2k possible sets of eigentuples thus extending to the multiparameter case the well known theorem concerning 1-parameter periodic equation.
1979 ◽
Vol 84
(3-4)
◽
pp. 249-257
◽
1971 ◽
Vol 23
(4)
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pp. 699-703
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2002 ◽
Vol 132
(6)
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pp. 1333-1359
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1989 ◽
Vol 139
(2)
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pp. 465-476