Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A disconjugacy criterion of W. T. Reid for difference equations


Authors: Allan Peterson and Jerry Ridenhour
Journal: Proc. Amer. Math. Soc. 114 (1992), 459-468
MSC: Primary 39A10; Secondary 39A12, 39A70
MathSciNet review: 1081096
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Abstract: Our main result is a disconjugacy criterion for the selfadjoint vector difference equation $ Ly(t) \equiv \Delta [P(t - 1)\Delta y(t - 1)] + Q(t)y(t) = 0$. This result is the analogue of a famous result of W. T. Reid for the corresponding differential equations case. Unlike the differential equations case we will see there is an exceptional case in which, as we will show by counterexample, the conclusion of the main result is no longer valid. A disfocality criterion is also given. We believe these results are new even in the scalar case.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1081096-9
Keywords: Disconjugate, prepared solution, generalized zero, disfocal
Article copyright: © Copyright 1992 American Mathematical Society